x^x=14

find x

no easy algebraic way to do it. You'll have to use a graphical or numeric technique (bisection, Newton's method, etc.)

But, you know that

2^2 = 4
3^3 = 27

so, 2 < x < 3

2.6^2.6 = 11.99
2.7^2.7 = 14.61

so, 2.6 < x < 2.7

you can do this to get as close as you desire.

There is a function called W(x) which will solve the equation, but it is basically defined as the function which solves x^x = n.