We report XMM-Newton observations of two examples of an unclassified type of X-ray weak quasars from the Pu et al. survey of X-ray weak quasars in the Chandra archive, SDSS J083116.62+321329.6 at z = 1.797 and SDSS J142339.87+042041.1 at z = 1.702. They do not belong to the known populations of X-ray weak quasars that show broad absorption lines, weak ultraviolet (UV) broad emission lines, or red optical/UV continua. Instead, they display typical quasar UV spectra and spectral energy distributions. In the XMM-Newton observations, both quasars show nominal levels of X-ray emission with typical quasar X-ray spectral shapes (power-law photon indices of 1.99-0.23+0.27 and 1.86-0.14+0.15 ), displaying strong X-ray variability compared to the archival Chandra data (variability factors of 4.0-1.4+1.6 and 9.0-3.8+7.4 in terms of the 2 keV flux density). Simultaneous optical (rest-frame UV) spectra indicate no strong variability compared to the archival spectra. Long-term optical/UV and infrared light curves do not show any substantial variability either. We consider that the X-ray weakness observed in the Chandra data is due to X-ray obscuration from a small-scale dust-free absorber, likely related to accretion-disk winds. Such X-ray weak/absorbed states are probably rare in typical quasars, and thus both targets recovered to X-ray nominal-strength states in the XMM-Newton observations.