Energy levels of electrons in an arbitrary element?

Let's say I want to calculate the wavelength of the photon emitted when an electron of an arbitrary element (let's say Carbon) drops from $n=4$ to $n=3$ . Correct me if I'm wrong, but I think I would have to find the change in the electron's energy value $\Delta E = E_i - E_f$ , set that equal to $hc/\lambda$ and solve for the wavelength ( $\lambda$ ). How could I find $E_f$ and $E_i$ ? My textbook gives Bohr's Equation but it also says that it fails to generalize, it only works for singular electrons and is kind of inaccurate outside of hydrogen. Does there exist a general equation to find these values?