To solve this algebraically, you have to use the Lambert W function

Lambert W function - Wikipedia, the free encyclopedia

Here are some other examples where the Lambert W function is needed.

http://www.mathhelpforum.com/math-he...-equation.html

http://www.mathhelpforum.com/math-he...2-x-x-2-a.html

http://www.mathhelpforum.com/math-he...lving-eqn.html

Try searching Math Forum for other threads where the Lambert W function is needed.

Hope this helps. Have fun exploring the world of math.