Actually from my experience pse 10 works just fine on windows 8.
The list that Baljeet S. Juneja, posted is just for photoshop elements installs that adobe supports (windows 8 came out after pse 10)
and does not mean photoshop elements will not work on older or newer operating systems.
Your best bet is to just install the program from the dvd or download that you have and see if it works to your level of satisfaction, as you can always
unistall pse 10 if it doesn't and upgrade to pse 11 if need be.
Right as per the link above, PSE 10 may work on Win8 but its not thoroughly tested.
The above list provides, all versions of PSE supported on respective OS'
From the Microsoft compatibilty pages, you get this
So others probably got it to work - as R_Kelly says above, it's worth a try.
Since Adobe no longer supports PSE 10 they would prefer you to buy the latest version. If you do decide to upgrade, look around for offers, the full version is sometimes cheaper than the upgrade version and both are the same.