  Solar flare X-ray spectra are typically dominated by thermal bremsstrahlung
emission in the soft X-ray ($\lesssim$10 keV) energy range; for hard X-ray
energies ($\gtrsim$30 keV), emission is typically non-thermal from beams of
electrons. The low-energy extent of non-thermal emission has only been loosely
quantified. It has been difficult to obtain a lower limit for a possible
non-thermal cutoff energy due to the significantly dominant thermal emission.
  Here we use solar flare data from the EUV Variability Experiment (EVE)
on-board the Solar Dynamics Observatory (SDO) and X-ray data from the Reuven
Ramaty High Energy Spectroscopic Imager (RHESSI) to calculate the Differential
Emission Measure (DEM). This improvement over the isothermal approximation and
any single-instrument DEM helps to resolve ambiguities in the range where
thermal and non-thermal emission overlap, and to provide constraints on the
low-energy cutoff.
  In the model, thermal emission is from a DEM that is parametrized as multiple
gaussians in $Log(T)$. Non-thermal emission results from a photon spectrum
obtained using a thick-target emission model. Spectra for both instruments are
fit simultaneously in a self-consistent manner.
  Our results have been obtained using a sample of 52 large (GOES X- and
M-class) solar flares observed between February 2011 and February 2013. It
turns out that it is often possible to determine low-energy cutoffs early (in
the first two minutes) during large flares. Cutoff energies are typically low,
less than 10 keV, with most values of the lower limits in the 5--7 keV range.
