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We report the confirmation of a TESS-discovered transiting super-Earth planet orbiting a mid-G star, HD 307842 (TOI-784). The planet has a period of 2.8 days, and the radial velocity (RV) measurements constrain the mass to be 9.67+0.83/-0.82 [Earth Masses]. We also report the discovery of an additional planet candidate on an outer orbit that is most likely non-transiting. The possible periods of the planet candidate are approximately 20 to 63 days, with the corresponding RV semi-amplitudes expected to range from 3.2 to 5.4 m/s and minimum masses from 12.6 to 31.1 [Earth Masses]. The radius of the transiting planet (planet b) is 1.93+0.11/-0.09 [Earth Radii], which results in a mean density of 7.4+1.4/-1.2 g/cm^3 suggesting that TOI-784b is likely to be a rocky planet though it has a comparable radius to a sub-Neptune. We found TOI-784b is located at the lower edge of the so-called ``radius valley'' in the radius vs. insolation plane, which is consistent with the photoevaporation or core-powered mass loss prediction. The TESS data did not reveal any significant transit signal of the planet candidate, and our analysis shows that the orbital inclinations of planet b and the planet candidate are 88.60+0.84/-0.86 degrees and <= 88.3-89.2 degrees, respectively. More RV observations are needed to determine the period and mass of the second object, and search for additional planets in this system.