Here are few of my proposals in your contest with different styles of letterform mark type of logos/icons interpreting the initial letters "EG"..As you can see that I've simply customized it with a circle but the letters still recognizable & most special thing with that is every part is equally balanced from every side, I mean from left OR right.
Unique, memorable, clean, modern & professional logos would be good & easy for web, print & etc..These logos would work great on both white(or light color) & black(or dark color) backgrounds..You can also use these logos as a stand alone icon for your web-fevicon, mobile-apps OR etc separately..I hope you like it..Any suggestion?