You do not have to install Java EE (J2EE) if all that you need is simple web development using JSP. Tomcat has a jar file that you can use to develop web applications using Servlet and JSP. The Java EE SDK that you downloaded has a Java EE certified Application Server unlike Tomcat which is a Servlet container.
From your post it looks like you downloaded Java EE 1.4 bundle that has Java SE 5.0 (J2SE 1.5). In order to use the bundled Java SE you need to override the default value of JAVA_HOME set by Fedora. You can do so by adding the following line of code to ~/.bashrc or ~/.bash_profile
The bundled Java SE should be in a directory under /usr/java/j2ee in your case.
If you want to know which java and javac are used issue the following command
Please note that changes to one of .bashrc and .bash_profile takes place only when you start a new session. Sorry but I cannot recall which one is that.
BTW, which version of Tomcat do you have? If you want to use Java SE 5.0 you need to download Tomcat 5.5.x. Tomcat 5.0.x works with Java SE 1.4.