There is no way to know on the server-side (unless you are using some JavaScript to send a message to the server) that the browser has closed. How could there be? Think of how HTTP works – everything is request and response.
However, the application server will track when Sessions are active and will even tell you when a Session has been destroyed (such as due to time-out). Take a look at this page to see how to configure a HttpSessionListener to receive these events. Then you can simply keep track of the number of active sessions.
The number of active sessions will lag behind the actual number of current users, since some period of (configurable) time has to elapse before a session is timed out; however, this should be somewhat close (you can lower the session-timeout to increase the accuracy) and it is a lot cleaner and easier than 1) tracking Sessions yourself or 2) sending some asynchronous JavaScript to the server when a browser is closed (which is not guaranteed to be sent).