Hello Cecil,
Java EE means you need an application server. Some of the popular
open
source ones I know are:
- Apache Tomee - http://tomee.apache.org/
- GlassFish - https://glassfish.java.net/
- JBoss WildFly - http://wildfly.org/
From what I know, none of them support JEE8 atm (not yet released).
All of them support JEE 6, and a few JEE 7. You will find that
information on each project page.
Unfortunately, they are not present in Debian. The reason, IMHO, they
have a lot of dependencies and are quite hard to package/maintain.
I recommend you start with Apache Tomee for JEE 6. I had quite good
experience with it.