You should go to the Help option => Install new Software, select the first link (assume that you have the latest version), although select the last option in the list XML, JAVA EE, hence, the Java EE will be available to your Eclipse
The next step is to install Tomcat to your Eclipse, first of all, you'd better go to the official Tomcat's website, download the version that you want, next, you should set up the downloaded Tomcat in your Eclipse, it needs some configuration
You don't necessarily need a Java EE server to support as Java EE application.
If you would end-up only deploying a single application on the server, then maybe consider a microservice framework like Quarkus, Payara, Helidon, OpenLiberty, etc. The frameworks typically support the most needed/useful technologies from Jakarta EE, plus additional capabilities from MicroProfile, and are way easier to deploy (usually just a single jar with business logic, and a collection of supporting library jars).
JEE is just Java with extra steps. Specifically, there are libraries that augment the core Java libraries to provide JEE functionality. JEE itself is a very broad platform, and although we tend to think of it in terms of web applications, it also supports database persistence, messaging systems, email services, and a lot more.
For webapps, there are two classes of servers: the so-called full-stack servers and the reduced-capability servers. Full Stack means pretty much all of JEE. The primary reduced-capability servers are Tomcat and jetty. The difference is that Tomcat/jetty provide servlet and JSP support built-in and that's about it. JEE features like the Java Persistence Architecture/Enterprise JavaBeans, JavaServer Faces and so forth are not built into the server the way they are in a full-stack system. That's fine, you get a lighter server that way, and some of the more common features can be added to Tomcat/jetty webapps via extra libraries added to the web application itself.
Eclipse supports JEE applications, but it's all done via Eclipse plugins. Eclipse itself is pretty minimal, so the Eclipse JEE distribution has a set of pre-installed plugins to support JEE. Some of which I like better than others. In particular, I heartily dislike the WTP webapp server manager plugin. It's supposed to permit the control of JEE servers such as Tomcat. but it makes a real mess of Tomcat, so I ignore that part and have historically used a similar but different plugin named Mongrel that maybe isn't quite as tightly integrated, but interacts more cleanly.
Eclipse supports "project facets" and they can assist in working with JEE.
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