I believe in this case x can't be a whole number which means you will have to go through some trial and errors.
when x is 1.5, x^x=1.8371173070873836.... which is obviously smaller than 2
when x=1.6 x^x=2.1212505710975916.... which is bigger than 2
now we know that x is between 1.5 and 1.6
you can always write "x is bigger than 1.5 but smaller than 1.6" or you can do some trial and errors to get more accurate answer such as x=1.559610.....
but i believe you won't be able to get an accurate answer as it is an infinite decimal.
hope it helped :)