  We describe meromorphic solutions to the equations
$f^n(z)+\left(f'\right)^n(z)=e^{\alpha z+\beta}$ and $f^n(z)+f^n(z+c)=e^{\alpha
z+\beta}$ ($c\neq0$) over the complex plane $\mathbf{C}$ for integers $n\geq1$.
