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The game crashed whilst there was a severe problem during mod loading that has caused the game to fail
Error: cpw.mods.fml.common.LoaderException: java.lang.NoSuchMethodError: appeng.api.IAppEngApi.definitions()Lappeng/api/definitions/IDefinitions;

---- Minecraft Crash Report -------- Minecraft Crash Report ----// Hi. I'm Minecraft, and I'm a crashaholic.
Time: 2/27/18 8:53 PMDescription: There was a severe problem during mod loading that has caused the game to fail
cpw.mods.fml.common.LoaderException: java.lang.NoSuchMethodError: appeng.api.IAppEngApi.definitions()Lappeng/api/definitions/IDefinitions; at cpw.mods.fml.common.LoadController.transition(LoadController.java:163) at cpw.mods.fml.common.Loader.initializeMods(Loader.java:744) at cpw.mods.fml.client.FMLClientHandler.finishMinecraftLoading(FMLClientHandler.java:311) at net.minecraft.client.Minecraft.func_71384_a(Minecraft.java:552) at net.minecraft.client.Minecraft.func_99999_d(Minecraft.java:878) at net.minecraft.client.main.Main.main(SourceFile:148) at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method) at sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62) at sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43) at java.lang.reflect.Method.invoke(Method.java:483) at net.minecraft.launchwrapper.Launch.launch(Launch.java:135) at net.minecraft.launchwrapper.Launch.main(Launch.java:28)Caused by: java.lang.NoSuchMethodError: appeng.api.IAppEngApi.definitions()Lappeng/api/definitions/IDefinitions; at micdoodle8.mods.galacticraft.core.recipe.RecipeManagerGC.addAppEngRecipes(RecipeManagerGC.java:663) at micdoodle8.mods.galacticraft.core.recipe.RecipeManagerGC.loadRecipes(RecipeManagerGC.java:53) at micdoodle8.mods.galacticraft.core.GalacticraftCore.postInit(GalacticraftCore.java:519) at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method) at sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62) at sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43) at java.lang.reflect.Method.invoke(Method.java:483) at cpw.mods.fml.common.FMLModContainer.handleModStateEvent(FMLModContainer.java:532) at sun.reflect.GeneratedMethodAccessor2.invoke(Unknown Source) at sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43) at java.lang.reflect.Method.invoke(Method.java:483) at com.google.common.eventbus.EventSubscriber.handleEvent(EventSubscriber.java:74) at com.google.common.eventbus.SynchronizedEventSubscriber.handleEvent(SynchronizedEventSubscriber.java:47) at com.google.common.eventbus.EventBus.dispatch(EventBus.java:322) at com.google.common.eventbus.EventBus.dispatchQueuedEvents(EventBus.java:304) at com.google.common.eventbus.EventBus.post(EventBus.java:275) at cpw.mods.fml.common.LoadController.sendEventToModContainer(LoadController.java:212) at cpw.mods.fml.common.LoadController.propogateStateMessage(LoadController.java:190) at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method) at sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:62) at sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43) at java.lang.reflect.Method.invoke(Method.java:483) at com.google.common.eventbus.EventSubscriber.handleEvent(EventSubscriber.java:74) at com.google.common.eventbus.SynchronizedEventSubscriber.handleEvent(SynchronizedEventSubscriber.java:47) at com.google.common.eventbus.EventBus.dispatch(EventBus.java:322) at com.google.common.eventbus.EventBus.dispatchQueuedEvents(EventBus.java:304) at com.google.common.eventbus.EventBus.post(EventBus.java:275) at cpw.mods.fml.common.LoadController.distributeStateMessage(LoadController.java:119) at cpw.mods.fml.common.Loader.initializeMods(Loader.java:742) ... 10 more

A detailed walkthrough of the error, its code path and all known details is as follows:---------------------------------------------------------------------------------------
-- System Details --Details: Minecraft Version: 1.7.10 Operating System: Windows 8.1 (amd64) version 6.3 Java Version: 1.8.0_25, Oracle Corporation Java VM Version: Java HotSpot(TM) 64-Bit Server VM (mixed mode), Oracle Corporation Memory: 235849128 bytes (224 MB) / 905969664 bytes (864 MB) up to 6442450944 bytes (6144 MB) JVM Flags: 8 total; -XX:HeapDumpPath=MojangTricksIntelDriversForPerformance_javaw.exe_minecraft.exe.heapdump -Xmx6G -XX:+UnlockExperimentalVMOptions -XX:+UseG1GC -XX:G1NewSizePercent=20 -XX:G1ReservePercent=20 -XX:MaxGCPauseMillis=50 -XX:G1HeapRegionSize=16M AABB Pool Size: 0 (0 bytes; 0 MB) allocated, 0 (0 bytes; 0 MB) used IntCache: cache: 0, tcache: 0, allocated: 0, tallocated: 0 FML: MCP v9.05 FML v7.10.99.99 Minecraft Forge 10.13.4.1614 Optifine OptiFine_1.7.10_HD_U_E3 34 mods loaded, 34 mods active States: 'U' = Unloaded 'L' = Loaded 'C' = Constructed 'H' = Pre-initialized 'I' = Initialized 'J' = Post-initialized 'A' = Available 'D' = Disabled 'E' = Errored UCHIJ mcp{9.05} [Minecraft Coder Pack] (minecraft.jar) UCHIJ FML{7.10.99.99} [Forge Mod Loader] (forge-1.7.10-10.13.4.1614-1.7.10.jar) UCHIJ Forge{10.13.4.1614} [Minecraft Forge] (forge-1.7.10-10.13.4.1614-1.7.10.jar) UCHIJ appliedenergistics2-core{rv1-stable-1} [AppliedEnergistics2 Core] (minecraft.jar) UCHIJ CodeChickenCore{1.0.7.47} [CodeChicken Core] (minecraft.jar) UCHIJ Micdoodlecore{} [Micdoodle8 Core] (minecraft.jar) UCHIJ NotEnoughItems{1.0.5.120} [Not Enough Items] (NotEnoughItems-1.7.10-1.0.5.120-universal (1).jar) UCHIJ <CoFH ASM>{000} [CoFH ASM] (minecraft.jar) UCHIJ CoFHCore{1.7.10R3.1.4} [CoFH Core] (CoFHCore-[1.7.10]3.1.4-329.jar) UCHIJ advancedgenetics{1.5.9} [Advanced Genetics] (advancedgenetics-1.7.10-1.5.9.jar) UCHIJ appliedenergistics2{rv1-stable-1} [Applied Energistics 2] (appliedenergistics2-rv1-stable-1.jar) UCHIJ Backpack{2.0.1} [Backpack] (Backpacks-Mod.jar) UCHIJ FLabsBF{4.3} [Better Furnaces] (Better-Furnaces-Mod-1.7.10.jar) UCHIJ BiomesOPlenty{2.1.0} [Biomes O' Plenty] (BiomesOPlenty-1.7.10-2.1.0.1548-universal.jar) UCHIJ qmunitylib{1.0} [QmunityLib] (QmunityLib-1.7.10-0.1.114-universal.jar) UCHIJ bluepower{0.2.962} [Blue Power] (BluePower-1.7.10-0.2.962-universal.jar) UCHIJ BuildCraft|Core{7.1.23} [BuildCraft] (buildcraft-7.1.23.jar) UCHIJ BuildCraft|Transport{7.1.23} [BC Transport] (buildcraft-7.1.23.jar) UCHIJ BuildCraft|Factory{7.1.23} [BC Factory] (buildcraft-7.1.23.jar) UCHIJ BuildCraft|Silicon{7.1.23} [BC Silicon] (buildcraft-7.1.23.jar) UCHIJ BuildCraft|Robotics{7.1.23} [BC Robotics] (buildcraft-7.1.23.jar) UCHIJ BuildCraft|Energy{7.1.23} [BC Energy] (buildcraft-7.1.23.jar) UCHIJ BuildCraft|Builders{7.1.23} [BC Builders] (buildcraft-7.1.23.jar) UCHIJ chisel{2.9.5.11} [Chisel] (Chisel-2.9.5.11 (2).jar) UCHIJ Forestry{4.2.6.54} [Forestry for Minecraft] (forestry_1.7.10-4.2.6.54.jar) UCHIJ fossil{1.7.10 Build 7.0.1} [Fossils and Archeology Revival] (Fossils_Archeology_Revival-1.7.10_Build-7.0.1.jar) UCHIE GalacticraftCore{3.0.12} [Galacticraft Core] (Galacticraft-Mod-1.7.10 (1).jar) UCHIJ iChunUtil{4.2.3} [iChunUtil] (iChunUtil-4.2.3.jar) UCHIJ IronChest{6.0.62.742} [Iron Chest] (ironchest-1.7.10-6.0.62.742-universal.jar) UCHIJ Mantle{1.7.10-0.3.2.jenkins191} [Mantle] (Mantle-1.7.10-0.3.2b.jar) UCHIJ NetherOres{1.7.10R2.3.2B1} [Nether Ores] (NetherOres-[1.7.10]2.3.2B1-25.jar) UCHIJ ProjectE{1.7.10-PE1.10.1} [ProjectE] (ProjectE-1.7.10-PE1.10.1.jar) UCHIJ Waila{1.5.10} [Waila] (Waila-1.5.10_1.7.10.jar) UCHIJ TConstruct{1.7.10-1.8.4.build939} [Tinkers' Construct] (TConstruct-1.7.10-1.8.4a.jar) GL info: ' Vendor: 'NVIDIA Corporation' Version: '4.6.0 NVIDIA 388.13' Renderer: 'GeForce GT 630/PCIe/SSE2' CoFHCore: -[1.7.10]3.1.4-329 AE2 Version: stable rv1-stable-1 for Forge 10.13.0.1187 Mantle Environment: DO NOT REPORT THIS CRASH! Unsupported mods in environment: optifine NetherOres: -[1.7.10]2.3.2B1-25 TConstruct Environment: Environment healthy. Chisel: Errors like "[FML]: Unable to lookup ..." are NOT the cause of this crash. You can safely ignore these errors. And update forge while you're at it. Forestry : Warning: You have mods that change the behavior of Minecraft, ForgeModLoader, and/or Minecraft Forge to your client: OptifineThese may have caused this error, and may not be supported. Try reproducing the crash WITHOUT these mods, and report it then. AE2 Integration: IC2:OFF, RotaryCraft:OFF, RC:OFF, BC:OFF, MJ6:OFF, MJ5:OFF, RF:ON, RFItem:ON, MFR:OFF, DSU:OFF, FZ:OFF, FMP:OFF, RB:OFF, CLApi:OFF, Waila:ON, InvTweaks:OFF, NEI:ON, CraftGuide:OFF, Mekanism:OFF, ImmibisMicroblocks:OFF, BetterStorage:OFF OptiFine Version: OptiFine_1.7.10_HD_U_E3 Render Distance Chunks: 8 Mipmaps: 4 Anisotropic Filtering: 1 Antialiasing: 0 Multitexture: false Shaders: null OpenGlVersion: 4.6.0 NVIDIA 388.13 OpenGlRenderer: GeForce GT 630/PCIe/SSE2 OpenGlVendor: NVIDIA Corporation CpuCount: 4

I don't think it's a core mod issue, I think it's conflicting with a too-old version of AE2:

Caused by: java.lang.NoSuchMethodError: appeng.api.IAppEngApi.definitions()Lappeng/api/definitions/IDefinitions; at micdoodle8.mods.galacticraft.core.recipe.RecipeManagerGC.addAppEngRecipes(RecipeManagerGC.java:663)

UCHIJ appliedenergistics2{rv1-stable-1} [Applied Energistics 2] (appliedenergistics2-rv1-stable-1.jar)

I can't tell exactly what build of GC the OP is using, but I suggest trying a newer build of AE2, such as rv2-stable-10 or rv3-beta-6.