Revese proxy for two servers behind one IP (no replies)

I think I need to setup a reverse proxy to do what I want to do.

I have two servers. The public IP points to our router which in turn forwards the request to server A running apache with a few sites.
I also have another server running a couple of other sites internally that I want to make available on the public IP. I have already setup my DNS provider at GoDaddy to go into our public IP. however they are only forwarded to the one server. I need that server to relay those requests to the apache on server B.

I think the reverse proxy is how to do that but I'm struggling to learn how to do that.

Here is a diagram for reference: [imgur.com]