Derive an equation with Faraday's law

Question

I need to find what equation is satisfied by $\Psi(x,y,z,t)$ given that $\textbf{B} = \nabla \times (\textbf{z} \Psi)$ and $\textbf{E} = -\textbf{z} \frac{\partial \Psi}{\partial t}$ while making use of of Faraday's law $ \nabla \times \textbf{E} = -\frac{\partial \textbf{B}}{\partial t}$ (with z the unity vector in the z direction). I calculated all these conditions but I can't derive a proper equation.