I wouldn't be too surprised if you can't find a PPA, etc. to work with 7.10, because it relies on someone maintaining it.
You can download firefox yourself (www.firefox.com). You'll get a package which has already been compiled, and you can extract it to '/opt/firefox' and make a link to the executable.
Firefox can be a little funny with its dependencies, however, and you may find yourself needing extra libraries outside of the 7.10 repositories. In short, this could end up becoming quite involved; and I wouldn't attempt it if you're not too sure about the more detailed workings of Ubuntu.
Note that it will now be up to you to keep your browser updated, as you're outside the reach of aptitude, etc. and with something like a web browser, i recommend you keep an eye out for new versions.