  Simultaneous solar flare observations with SDO and RHESSI provide spatially
resolved information about hot plasma and energetic particles in flares. RHESSI
allows the properties of both hot (> 8 MK) thermal plasma and nonthermal
electron distributions to be inferred, while SDO/AIA is more sensitive to lower
temperatures. We present and implement a new method to reconstruct electron
distribution functions from SDO/AIA data. The combined analysis of RHESSI and
AIA data allows the electron distribution function to be inferred over the
broad energy range from ~0.1 keV up to a few tens of keV. The analysis of two
well observed flares suggests that the distributions in general agree to within
a factor of three when the RHESSI values are extrapolated into the intermediate
range 1-3 keV, with AIA systematically predicting lower electron distributions.
Possible instrumental and numerical effects, as well as potential physical
origins for this discrepancy are discussed. The inferred electron distribution
functions in general show one or two nearly Maxwellian components at energies
below ~ 15 keV and a non-thermal tail above.
