  The number of super-Earth and mini-Neptune planet discoveries has increased
significantly in the last two decades thanks to transit and radial velocity
surveys. When it is possible to apply both techniques, we can characterise the
internal composition of exoplanets, which in turn provides unique insights on
their architecture, formation and evolution.
  We performed a combined photometric and radial velocity analysis of TOI-238
(TYC 6398-132-1), which has one short-orbit super-Earth planet candidate
announced by NASA's TESS team. We aim to confirm its planetary nature using
radial velocities taken with the ESPRESSO and HARPS spectrographs, to measure
its mass and to detect the presence of other possible planetary companions. We
carried out a joint analysis by including Gaussian processes and Keplerian
orbits to account for the stellar activity and planetary signals
simultaneously.
  We detected the signal induced by TOI-238 b in the radial velocity
time-series, and the presence of a second transiting planet, TOI-238 c, whose
signal appears in RV and TESS data. TOI-238 b is a planet with a radius of
1.402$^{+0.084}_{-0.086}$ R$_{\oplus}$ and a mass of 3.40$^{+0.46}_{-0.45}$
M$_{\oplus}$. It orbits at a separation of 0.02118 $\pm$ 0.00038 AU of its host
star, with an orbital period of 1.2730988 $\pm$ 0.0000029 days, and has an
equilibrium temperature of 1311 $\pm$ 28 K. TOI-238 c has a radius of 2.18$\pm$
0.18 R$_{\oplus}$ and a mass of 6.7 $\pm$ 1.1 M$_{\oplus}$. It orbits at a
separation of 0.0749 $\pm$ 0.0013 AU of its host star, with an orbital period
of 8.465652 $\pm$ 0.000031 days, and has an equilibrium temperature of 696
$\pm$ 15 K. The mass and radius of planet b are fully consistent with an
Earth-like composition, making it likely a rocky super-Earth. Planet c could be
a water-rich planet or a rocky planet with a small H-He atmosphere.
