We report the discoveries of the two-image gravitationally lensed quasars, SDSS J0746+4403 and SDSS J1406+6126, selected from the Sloan Digital Sky Survey (SDSS). SDSS J0746+4403, which will be included in our lens sample for statistics and cosmology, has a source redshift of z_s=2.00, an estimated lens redshift of z_l~0.3, and an image separation of 1.08. SDSS J1406+6126 has a source redshift of z_s=2.13, a spectroscopically measured lens redshift of z_l=0.27, and an image separation of 1.98. We find that the two quasar images of SDSS J1406+6126 have different intervening MgII absorption strengths, which are suggestive of large variations of absorbers on kpc scales. The positions and fluxes of both the lensed quasar systems are easily reproduced by simple mass models with reasonable parameter values. These objects bring to 18 the number of lensed quasars that have been discovered from the SDSS data.