We report the discovery of HIP-97166b (TOI-1255b), a transiting sub-Neptune on a 10.3day orbit around a K0 dwarf 68pc from Earth. This planet was identified in a systematic search of TESS Objects of Interest for planets with eccentric orbits, based on a mismatch between the observed transit duration and the expected duration for a circular orbit. We confirmed the planetary nature of HIP-97166b with ground-based radial-velocity measurements and measured a mass of M_b_=20{+/-}2M{Earth} along with a radius of R_b_=2.7{+/-}0.1R{Earth} from photometry. We detected an additional nontransiting planetary companion with M_c_sini=10{+/-}2M{Earth} on a 16.8day orbit. While the short transit duration of the inner planet initially suggested a high eccentricity, a joint RV-photometry analysis revealed a high impact parameter b=0.84{+/-}0.03 and a moderate eccentricity. Modeling the dynamics with the condition that the system remain stable over >10^5^ orbits yielded eccentricity constraints e_b_=0.16{+/-}0.03 and e_c_<0.25. The eccentricity we find for planet b is above average for the small population of sub-Neptunes with well-measured eccentricities. We explored the plausible formation pathways of this system, proposing an early instability and merger event to explain the high density of the inner planet at 5.3{+/-}0.9g/cc as well as its moderate eccentricity and proximity to a 5:3 mean-motion resonance.