Creating and computing functions

So you're looking for a function g such that g(x^(x^x)) = x?

y = x^(x^x)
ln y = x^x ln x

ln ln y = ln (x^x ln x) = x ln x ln ln x.

Call me crazy, but I don't know whether there exists an explicit expression for x in terms of elementary functions.

To approximate the function in code, several options exist. All of them will boil down to iteratively building up a solution, though. Newton's method could probably be used, or, more simply, just start with 0000000000.00000000000 and, starting at the left, increase a 10's place digit until the x^x^x gets too big, go back to the previous version, and go to a lower power of 10, and continue until you have as much precision as you want. Since x^x^x will grow pretty insanely quickly, you shouldn't have to check much higher than 10.