Microsoft Office Enterprise, as opposed to your posted name of "Microsoft Enterprise Office" is a genuine MS Office product, in fact I have just bought it (not installed yet) through my wife's work (NHS) for £9. click here
When you have it installed alongside an older version of MS Office, it does indeed "try to install itself" when you try to start it, in fact most MS Office products do that when there is more than one version installed on the same PC. Have you maybe installed a trial of MOE or had a version pre-installed on your PC, or maybe you're using a work PC?
If none of the above senarios apply, and you think your "Microsoft Enterprise Office" is a rogue program, try running a scan with MBAM. click here