@mftuchman - As far as I am aware there is no keyboard shortcut for this. EG 7.15 however remembers the workplace layout from session to session so if you finish your EG session in side-by-side mode, that is how it will show in your next session.
EG 8.1 / 8.2 uses tabs for each project / program so the paradigm is quite different. You can still get the side-by-side layout by using the "new vertical tab group" menu option. Again I'm not aware of any keyboard shortcut for this.