  Deriving a well-constrained differential emission measure (DEM) distribution
for solar flares has historically been difficult, primarily because no single
instrument is sensitive to the full range of coronal temperatures observed in
flares, from $\lesssim$2 to $\gtrsim$50 MK. We present a new technique,
combining extreme ultraviolet (EUV) spectra from the EUV Variability Experiment
(EVE) onboard the Solar Dynamics Observatory with X-ray spectra from the Reuven
Ramaty High Energy Solar Spectroscopic Imager (RHESSI), to derive, for the
first time, a self-consistent, well-constrained DEM for jointly-observed solar
flares. EVE is sensitive to ~2-25 MK thermal plasma emission, and RHESSI to
$\gtrsim$10 MK; together, the two instruments cover the full range of flare
coronal plasma temperatures. We have validated the new technique on artificial
test data, and apply it to two X-class flares from solar cycle 24 to determine
the flare DEM and its temporal evolution; the constraints on the thermal
emission derived from the EVE data also constrain the low-energy cutoff of the
non-thermal electrons, a crucial parameter for flare energetics. The DEM
analysis can also be used to predict the soft X-ray flux in the poorly-observed
~0.4-5 nm range, with important applications for geospace science.
