- Recently, Dial et al. presented measurements of the tunneling density of states into the bulk of a two dimensional electron gas under strong magnetic fields. Several high energy features appear in the measured spectrum showing a distinct dependence on filling factor and a unique response to temperature. We present a quantitative account of the observed structure, and argue it results from the repulsive Coulomb interactions between the tunneling electron and states localized at disorder potential wells. The quenching of the kinetic energy by the applied magnetic field leads to an electron addition spectrum that is primarily determined by the external magnetic field and is nearly independent of the disorder potential. Using a Hartree-Fock model we reproduce the salient features of the observed structure.