Is it possible to rearrange the right side to look like a straightforward function as
$$x = f(y)$$?
I'm not clear on what you are asking. Assuming w and z are variables then the answer is no. If w and z are constants then you could rearrange this as
$\displaystyle x = e^{C(z - w)} \cdot e^{-Cy} = K e^{-Cy}$ where $\displaystyle K = e^{C(z - w)}$ is a constant.