  We obtained $XMM-Newton$ observations of two highly luminous dust-reddened
quasars, F2M1113+1244 and F2M1656+3821, that appear to be in the early,
transitional phase predicted by merger-driven models of quasar/galaxy
co-evolution. These sources have been well-studied at optical through
mid-infrared wavelengths and are growing relatively rapidly, with Eddington
ratios $>30\%$. Their black hole masses are relatively small compared to their
host galaxies placing them below the $M_{\rm BH} - L_{\rm bulge}$ relation. We
find that for both sources, an absorbed power-law model with $1-3\%$ of the
intrinsic continuum scattered or leaked back into the line-of-sight best fits
their X-ray spectra. We measure the absorbing column density ($N_H$) and
constrain the dust-to-gas ratios in these systems, finding that they lie well
below the Galactic value. This, combined with the presence of broad emission
lines in their optical and near-infrared spectra, suggests that the dust
absorption occurs far from the nucleus, in the host galaxy, while the X-rays
are mostly absorbed in the nuclear, dust-free region within the sublimation
radius. We also compare the quasars' absorption-corrected, rest-frame X-ray
luminosities ($2-10$ keV) to their rest-frame infrared luminosities (6$\mu$m)
and find that red quasars, similar to other populations of luminous obscured
quasars, are either underluminous in X-rays or overluminous in the infrared.
