Since RHS is even. So LHS is also even integer so either both x and y should be even or both should be odd integer.
Now x4−y4=(x−y)(x+y)(x2+y2)
(x−y),(x+y),(x2+y2) must be an even integer
Therefore (x−y),(x+y),(x2+y2) must be divisible by 8
But RHS is not divisible by 8
So given equation has no solution