Can you run WordPress on a MarketLive/Java EE server?

PHP is programming language and software that interprets and runs code written in that programming language. But PHP is not web server – software that responds to requests, puts together and sends pages to visitors.

If you are using web server that cannot use PHP then your only option is to add another web server that is capable of that. Which of course comes with setup and integration issues.

The low hanging fruit solution in your case would probably be setting up separate site under blog.yourdomain.com or something, with setup appropriate for WordPress and handle it separately from main site.