A technique is presented for inverting incoherent scatter radar (ISR) measurements of the auroral ionosphere to determine the incident electron energy spectrum. A linear model is constructed relating electron differential number flux to the volume production rate of ions, the latter derived from measured electron density profiles using a continuity equation. The forward model is inverted using the maximum entropy method (MEM). This implementation of ISR inversion was found to be remarkably robust to the principal sources of model and measurement uncertainty. The procedure was applied to high-resolution measurements (1.2 s × 1 km) by the Sondrestrom ISR recorded during an auroral surge. Analysis of bulk plasma properties in the recovered spectra suggested that the relationship between the characteristic energy and the net number flux was highly nonlinear during the onset of the auroral surge, an observation that can now be evaluated statistically. This perspective on the temporal behavior of the auroral acceleration region cannot be accessed through spaceborne measurements; ISR inversion thus constitutes a critical tool for addressing time-dependent coupling of the magnetosphere and ionosphere.