We report the discovery of the 1.008-d, ultrashort period (USP) super-Earth HD 213885b (TOI-141b) orbiting the bright (V= 7.9) star HD 213885 (TOI-141, TIC 403224672), detected using photometry from the recently launched TESS mission. Using FEROS, HARPS, and CORALIE radial velocities, we measure a precise mass of 8.8 ±0.6M⊙ for this 1.74±0.05R⊙ exoplanet, which provides enough information to constrain its bulk composition - similar to Earth's but enriched in iron. The radius, mass, and stellar irradiation of HD 213885b are, given our data, very similar to 55 Cancri e, making this exoplanet a good target to perform comparative exoplanetology of short period, highly irradiated super-Earths. Our precise radial velocities reveal an additional 4.78-d signal which we interpret as arising from a second, non-transiting planet in the system, HD 213885c, whose minimum mass of 19.9 ± 1.4 M⊙ makes it consistent with being a Neptune-mass exoplanet. The HD 213885 system is very interesting from the perspective of future atmospheric characterization, being the second brightest star to host an USP transiting super-Earth (with the brightest star being, in fact, 55 Cancri). Prospects for characterization with present and future observatories are discussed
