An inversion technique has been developed to recover LTE one-dimensional model photospheres for late-type stars from very high resolution, high signal-to-noise stellar line profiles. It is successfully applied to the Sun by using a set of clean Ti I, Ca I, Cr I, and Fe I normalized line profiles with accurate transition probabilities and taking advantage of the well understood collisional enhancement of the wings of the Ca I line at 6162 A. Line and continuum center-to-limb variations, continuum flux, and wings of strong metal lines are synthesized by means of the model obtained and are compared with solar observations, as well as with predictions from other well known theoretical and empirical solar models, showing the reliability of the inversion procedure. The prospects for and limitations of the application of this method to other late-type stars are discussed.