In 2008, coordinated radar-optical auroral observations were organized in Northern Scandinavia using the European Incoherent Scatter Radar (EISCAT) and the Auroral Large Imaging System (ALIS). A bright auroral arc was imaged on 5 March 2008 from four ground-based stations, remaining stable between 18:41 and 18:44 UT and coinciding with increased electron densities. This work presents a unified inversion framework deriving the electron energy spectrum from either optical (inline image 1NG(0,1) emission at 4278 Å) or radar (electron density) observations. An updated forward model of the ionosphere based on a 1-D kinetic Monte Carlo model is described, characterizing the linear system to invert. The 3-D blue volume emission rate is first estimated with an iterative reconstruction technique. Also presented is a novel way to calculate an accurate initial guess for auroral tomography taking into account the horizontal/vertical nonuniformity of the emission region. This technique supersedes the often-used Chapman profile as initial guess when high spatial resolution is needed. The second step, performed for the first time with ALIS optical observations, uses the forward model to retrieve from the emission rates the 2-D latitude/longitude map of the electron energy spectrum. The same model and inversion methods are finally applied to the EISCAT electron density profiles to derive the temporal energy spectrum of precipitating electrons along the magnetic zenith. Energy spectra from radar and optics are in good agreement. Results suggest that the arc is generated by a complex energy spectrum reminiscent of dispersive Alfvén waves with two main peaks (2.5, 6 keV) and a typical latitudinal width of 7.5 km.