We carried out numerical experiments on the evaluation of the possibilities of obtaining information about the brightness distributions for the components of eclipsing variables from the high-precision photometry data expected to be obtained from the planned satellites COROT and Kepler. We examined a simple model of an eclipsing binary with spherical components on circular orbits and a linear law of limb darkening. The solutions of light curves have been obtained both by fitting a nonlinear model by a number of parameters including the limb-darkening coefficients and by solving the ill-posed inverse problem of restoration of brightness distributions across the discs of stars using a priori information about the form of these functions. The obtained estimates show that, if the observational accuracy is 10-4, then the limb-darkening coefficients can be found with a relative error of approximately 0.01. The brightness distributions across the discs of components can be restored to nearly the same accuracy as well.