Question

What is this? e^(xy) + y^2 = sin(x + y)

Answer 1

What are you supposed to 'do' with it ?
There's a very simple reason why no 'solution' is possible:
In order to find a unique solution, you need as many equations
as variables.  This is one equation in two variables, so it has
infinitely many solutions ... pairs of numbers for 'x' and 'y' that
make the equation a true statement.

Here's one of them:          (π/2, 0) .