An intriguing pattern among exoplanets is the lack of detected planets between approximately 1.5R{Earth} and 2.0R{Earth}. One proposed explanation for this "radius gap" is the photoevaporation of planetary atmospheres, a theory that can be tested by studying individual planetary systems. Kepler-105 is an ideal system for such testing due to the ordering and sizes of its planets. Kepler-105 is a Sun-like star that hosts two planets straddling the radius gap in a rare architecture with the larger planet closer to the host star (Rb=2.53{+/-}0.07R{Earth}, Pb=5.41days, Rc=1.44{+/-}0.04R{Earth}, Pc=7.13days). If photoevaporation sculpted the atmospheres of these planets, then Kepler-105b would need to be much more massive than Kepler-105c to retain its atmosphere, given its closer proximity to the host star. To test this hypothesis, we simultaneously analyzed radial velocities and transit-timing variations of the Kepler-105 system, measuring disparate masses of Mb=10.8{+/-}2.3M{Earth} ({rho}b=3.68{+/-}0.84g/cm^3^) and Mc=5.6{+/-}1.2M{Earth} ({rho}c=10.4{+/-}2.39g/cm^3^). Based on these masses, the difference in gas envelope content of the Kepler-105 planets could be entirely due to photoevaporation (in 76% of scenarios), although other mechanisms like core-powered mass loss could have played a role for some planet albedos.