Linux doesn't have EDT, but there are scores of editors available. The only one that's guaranteed to be included in every UNIX version is vi---forget it, your sysadm must have installed something better. Probably the most popular editor is emacs, which can emulate EDT to a certain degree; jed is another editor that provides EDT emulation.
These two editors are particularly useful for editing program sources, since they have two features unknown to EDT: syntax hilighting and automatic indentation. Moreover, you can compile your programs from within the editor (command ESC-X compile); in case of a syntax error, the cursor will be positioned on the offending line. I bet that you'll never want to use the true blue EDT again.
If you have emacs: start it, then type ESC-X edt-emulation-on. Pressing ALT--X or ESC-X is emacs' way of issuing commands, like EDT's CTRL--Z. From now on, emacs acts like EDT apart from a few commands. Differences:
don't press CTRL--Z to issue commands (if you did, you stopped emacs. Type fg to resume it);
there's an extensive on-line help. Press CTRL-H ?, or CTRL-H T to start a tutorial;
to save a file, press CTRL-X CTRL-S;
to exit, press CTRL-X CTRL-C;
to insert a new file in a buffer, press CTRL-X CTRL-F, then CTRL-X B to switch among buffers.
If you have jed: ask your sysadm to configure jed properly. Emulation is already on when you start it; use the normal keypad keys, and press CTRL--H CTRL--H or CTRL-? to get help. Commands are issued in the same way as emacs'. In addition, there are some handy key bindings missing in the original EDT; key bindings can also be tailored to your own taste. Ask your sysadm.
In alternative, you may use another editor with a completely different interface. emacs in native mode is an obvious choice; another popular editor is joe, which can emulate other editors like emacs itself (being even easier to use) or the DOS editor. Invoke the editor as jmacs or jstar and press, respectively, CTRL-X H or CTRL-J to get online help. emacs and jed are much more powerful than good ol' EDT.