Office 365 is a subscription-based cloud service:
http://en.wikipedia.org/wiki/Microsoft_Office_365
So there's going to be a demand for money coming in order to maintain full use of the service.
I certainly wouldn't try installing Office 2010
over Office 365 but there's no reason why you can't simply uninstall Office 365 and then install Office 2010.
Alternatively why not install a free alternative to Microsoft Office anyway? OpenOffice is just as good and is increasingly used by public bodies who don't like paying lots of money to Microsoft:
https://www.openoffice.org/
OpenOffice does everything that Microsoft Office does and, with a few simple tweaks can be configured to automatically save files in Microsoft Office formats (rather than in its own native formats) so that they can be forwarded to Microsoft Office users without any problems:
http://voices.yahoo.com/how-set-openoffice-writer-save-as-microsoft-11017880.html