Monte-Carlo generator with photon jets radiation in collinear regions for the process eegg is described in detail. Radiative corrections in the first order of $alpha$ are treated exactly. Large leading logarithmic corrections coming from collinear re
gions are taken into account in all orders of $alpha$ by applying the Structure Function approach. Theoretical precision of the cross section with radiative corrections is estimated to be 0.2%. This process is considered as an additional tool to measure luminosity in forthcoming experiments with the CMD-3 detector at the $e^+e^-$ collider VEPP-2000.
