While there were various ways of re-opening closed tabs in Visual Studio 2010 and Visual Studio 2012, it appears that those plug-ins have not evolved into the Visual Studio
Ctrl+- should jump you back into the tab you closed. You may have to do that several times.
Also ALT+F+F is a quick way to jump to recent files, your file might be there. Keep holding ALT while pressing F twice.
Productivity Power Tools 2013 is now available for Visual Studio 2013.
Along with a bunch of other features, it still offers Edit.UndoClose
functionality as previous version had.
You can find the command under Tools->Options and give it whatever shortcut you want (Ctrl+Shift+T, in this case, to make it like a web browser re-open tab shortcut).