CodeChickenCore for Minecraft 1.7.10
What's the problem?
CodeChickenCore tries to download non-existing library file
Replace CodeChickenCore with unofficial version
Recommended method
GregTech New Horizons modpack developers published a patched CodeChickenCore and CodeChickenLib with some fixes. Replace your mods with CodeChickenCore Unofficial and CodeChickenLib Unofficial.
Find working CodeChickenLib
There is a corrupted CodeChickenLib
mod file in the mods/1.7.10
folder. You can try to find the original version somewhere in the Web and replace it. Unfortunately, we are not able to help with that.