= 1,

     = 3,

     = 9,

     = 27,

     = 81,

     = 243.


At this point, it should be clear that there is no need to consider degrees higher than  = 81.


Trial and error method gives two solutions

    27 + 81 = 108,   81 + 27 = 108,

that are

     +  = 108,   +  = 108.


So, possible pairs (x,y) are  (3,4)  and  (4,3).    ANSWER

Trial and error may not be obvious to you, so you
might try doing a little algebra to make it easier
to see what to do.  



Divide both sides by 33 by subtracting
3 from both exponents of 3 on the left:



Factor out 3x-3 on the left:



That reminds us a little of .

That would be the case if the power of 3 before the parentheses 
were equal to 1, and the power of 3 inside the parentheses were
31.  

Now we know that 30 = 1.  And we see that x = 3 would make that
exponent = 0.

So now all we need to do is find y so that y-x = 1.  Substituting 
x = 3,  y - 3 = 1, or y = 4.

So  x = 3 and y = 4 are the answers.  Checking:



Edwin

Commenting Ikleyn's post, equations involving variable exponents are not taught
in kindergarten.

Edwin