We reconstruct the energy distribution of electrons accelerated in the April 15, 2002 solar flare on the basis of the data from the IRIS X-ray spectrometer onboard the CORONAS-F satellite. We obtain the solution to the integral equations describing the transformation of the spectrum of X-ray photons during the recording and reconstruction of the spectrum of accelerated electrons in the bremsstrahlung source using the random search method and the Tikhonov regularization method. In this event, we detected a singularity in the electron spectrum associated with the existence of a local minimum in the energy range 40–60 keV, which cannot be detected by a direct method.