Question 1209508
.


As Edwin explained in his post, this equation has infinitely many solutions in real numbers,
therefore the problem's request, as it is given in the post, makes no sense.


The problem gets sense, if to ask about solutions in integer positive numbers.


Notice that 


        145 = 81 + 64 = 64 + 81,  


    or


        145 = {{{3^4}}} + {{{4^3}}} = {{{4^3}}} + {{{3^4}}}.


It gives two solutions in integer positive numbers


        (a)   x = 9, y = 16;


        (b)    x = 16, y = 9.



There are other solutions.  Consider this decomposition


        145 = 144 + 1 = 1 + 144.



It gives two more solutions in integer numbers


        (c)   x = {{{12^2}}}, y = 1;


        (d)    x = 1, y = {{{12^2}}}.