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.
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