Are you sure that is the correct problem? Just making sure cause i just took a shot at it and i cannot figure it out....
On a random note, a few years of college will teach you how to use the Lambert W function to solve these equations.
Lambert W function - Wikipedia, the free encyclopedia
These types of questions always pop up on the forum once in a while. I'll give links when I have the time.
Here's a link to a similar question that links to another similar question.
1 = (x + 2) e
-e__= - (x + 2) e____, where x >= -2
-x-2 = W-1( -e___)
x = -2 - W-1( -e___) (x >= -2)
where W-1 is the negative branch of order -1 of Lambert's W function. Go to Lambert W function - Wikipedia, the free encyclopedia to find out how to compute this branch; you can use W-1(x) = ln(-x) - ln(-ln(-x)) or something more complex, depending on the accuracy required