Help solve this specific linear schrodinger equation, please

$$\left[-\frac{1}{2}\nabla^2 - \frac{2}{r} + C\right]\phi(r) = E\phi(r)$$


where $C$ is a known function. I am just looking for some help on the strategy to solve explicitly for $\phi(r)$. One thing I am having trouble understanding is how we can solve this equation without expressing $\phi(r)$ in terms of $E$, but it seems like it is done all the time:
<http://chemwiki.ucdavis.edu/Physical_Chemistry/Quantum_Mechanics/05.5%3A_Particle_in_Boxes/Particle_in_a_1-dimensional_box>


Thanks!


