First of, just to make sure, type "java" in the terminal to assert if Java really is not installed. after that, check the official repos first.
If you get nothing, check this
, (a tutorial using a PPA) or this topic
(it links to a good tutorial for manual installation and also offers a script for automation).
NOTE: I haven't personally installed Java this way, so I can't vouch for any of these methods. But looking at the steps, it looks correct.
If you have problems, post here with detailed description of what you did so far.
Btw, does anyone know what would happen if one would use a package for a previous or future Mint version? Would it generally work?