We apply density-functional theory to study the expanded-FCC-to-condensed-FCC transition of a system of hard, spherical particles with a short-ranged attractive interaction, predicted recently by the simulations of Bolhuis and Frenkel (1994). Our approach is based on a non-perturbative treatment of the repulsive hard-core part of the potential, using the modified weighted density approximation (MWDA), and a mean-field approximation for the attractive part. We confirm by means of this simple theoretical treatment the existence of an isostructural solid-to-solid transition which terminates at a critical point, in quantitative agreement with the simulation data. We obtain, within this approximation, classical critical exponents for the continuous transition.