A novel method was developed for the extraction of short emission times of light particles from the projectile-like fragments in peripheral deep-inelastic collisions in the Fermi energy domain. We have taken an advantage of the fact that in the external Coulomb field particles are evaporated asymmetrically. It was possible to determine the emission times in the interval 50-500 fm/c using the backward emission anisotropy of alpha-particles relative to the largest residue, in the reaction 28Si + 112Sn at 50 MeV/nucleon. The extracted times are consistent with predictions based on the evaporation decay widths calculated with the statistical evaporation model generalized for the case of the Coulomb interaction with the target.