>I have tried hard to

>solve the problem but i couldnt do it. You probably tried to express the solution by means of the so-called elementary function, right? sin(x), cos(x), x^{n}, a^{x}, etc... This is impossible.

The solution to x^{x} = a is given by the Lambert function invent specifically for that purpose. See, for example,

https://mathworld.wolfram.com/LambertsW-Function.html