An intriguing pattern among exoplanets is the lack of detected planets between approximately 1.5 R⊕ and 2.0 R⊕. 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 ± 0.07 R⊕, Pb = 5.41 days, Rc = 1.44 ± 0.04 R⊕, Pc = 7.13 days). 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 ± 2.3 M⊕ (ρb = 3.68 ± 0.84 g cm−3) and Mc = 5.6 ± 1.2 M⊕ (ρc = 10.4 ± 2.39 g 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.