XENON10 is a dual phase liquid/gas Xe time-projection chamber (TPC) with 3D position imaging, for dark matter direct detection. It provides event-by-event discrimination of electron recoil events (background) from nuclear recoil events (expected signal). The primary scintillation signal (S1) and ionization signal (S2) are both functions of recoil energy and incident particle type. We describe new methods to determine the relative scintillation yield Leff, and the absolute ionization yield Qy for nuclear recoils in Xe. The threshold is ~2 keV recoil energy (keVr). The Leff determination is in agreement with recent theoretical predictions above 10 keVr. The Qy is determined in two ways, both in agreement with previous measurements, but with a factor of 10 lower energy threshold. Knowledge of both Leff and Qy is crucial for establishing the energy threshold of a liquid Xe TPC for nuclear recoils, which in turn establishes the ultimate sensitivity to rare-event particle interactions in which the visible energy is due to a recoiling target nucleus. The methods used should be applicable to other liquid noble gas detectors.