We have inferred the energy distribution of trapped ions in an electron beam ion trap (EBIT) from simulations of the spatial distribution of Fe^{13+} ions and a comparison with measured visible light images of the ion cloud. We simulated the cloud of Fe^{13+} ions by computing ion trajectories in the EBIT for different ion energy distributions used to initialize the trajectories. We then performed a least-squares fit to infer the ion energy distribution that best reproduced the measured ion cloud. These best-fit distributions were typically non-Maxwellian. For electron beam energies of 395-475 eV and electron beam currents of 1-9 mA, we find that the average ion energy is in the range of 10-300 eV. We also find that the average ion energy increases with increasing beam current approximately as 〈E〉≈25I_{e}eV, where I_{e} is the electron beam current in mA. We have also compared our results to Maxwell-Boltzmann-distribution ion clouds. We find that our best-fit non-thermal distributions have an 〈E〉 that is less than half that of the T from the best-fit Maxwell-Boltzmann distributions (〈E〉/q)/T=0.41±0.05.