  We predict that strong coupling between waveguide photons and excitons of
quantum well embedded into waveguide results in the formation of hybrid dark
and anti-dark light-matter solitons. Such temporal solitons exist due to
interplay between repulsive excitonic nonlinearity and giant group velocity
dispersion arising in the vicinity of excitonic resonance. Such fully
conservative states do not require external pumping to counteract losses and
form continuous families parameterized by the power-dependent phase shift and
velocity of their motion. Dark solitons are stable in the considerable part of
their existence domain, while anti-dark solitons are always unstable. Both
families exist outside forbidden frequency gap of the linear system.
