We report the discovery of the 1.008-day, ultra-short 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 $8.8pm0.6$ $M_oplus$ for this $1.74 pm 0.05$ $R_oplus$ exoplanet, which provides enough information to constrain its bulk composition, which is similar to Earths 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 $4.78$-day signal which we interpret as arising from a second, non-transiting planet in the system, HD 213885c (TOI-141c), whose minimum mass of $19.95pm 1.4$ $M_oplus$ 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 ultra-short period transiting super-Earth (with the brightest star being, in fact, 55 Cancri). Prospects for characterization with present and future observatories are discussed.
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