Question about using a transform to solve Laplace's equation

Question

I want to solve $\frac{\partial^2 u}{\partial x^2}+\frac{\partial^2 u}{\partial y^2}= 0$ subject to $u(0,y)=A$ for $0<y<\pi$, and $\frac{\partial u}{\partial y} |_{y=0}= 0 $, $\frac{\partial u}{\partial y} |_{y=\pi}=Be^{-x} $, $x>0$. I feel like there's not enough information for me to solve this problem, I am trying to use a Laplace transform in $x$. What am I missing? Thanks four your help!