Sorry about the wait, I just saw your message. The easiest way is probably to download MultiMC, create an instance for 1.7.10 and then copy the appropriate contents from the zip to the minecraft folder in the instance folder.
Edit: If someone has a better way, by all means comment with your method. I'm not sure if this is the easiest/best way.
Edit2: Forgot to mention that you'll need to install forge 10.13.2.1277 through MultiMC.