We report the development of a multipurpose differential x-ray calorimeter with a broad energy bandwidth. The absorber architecture is combined with a Bayesian unfolding algorithm to unfold high energy x-ray spectra generated in high-intensity laser-matter interactions. Particularly, we show how to extract absolute energy spectra and how our unfolding algorithm can reconstruct features not included in the initial guess. The performance of the calorimeter is evaluated via Monte Carlo generated data. The method accuracy to reconstruct electron temperatures from bremsstrahlung is shown to be 5% for electron temperatures from 1 to 50 MeV. We study bremsstrahlung generated in solid target interaction showing an electron temperature of 0.56 ± 0.04 MeV for a 700 μm Ti titanium target and 0.53 ± 0.03 MeV for a 50 μm target. We investigate bremsstrahlung from a target irradiated by laser-wakefield accelerated electrons showing an endpoint energy of 551 ± 5 MeV, inverse Compton generated x rays with a peak energy of 1.1 MeV, and calibrated radioactive sources. The total energy range covered by all these sources ranges from 10 keV to 551 MeV.