Aims: In this work, we discuss a way to combine High Dispersion Spectroscopy and High Contrast Imaging (HDS+HCI). For a planet located at a resolvable angular distance from its host star, the starlight can be reduced up to several orders of magnitude using adaptive optics and/or coronography. In addition, the remaining starlight can be filtered out using high-dispersion spectroscopy, utilizing the significantly different (or Doppler shifted) high-dispersion spectra of the planet and star. In this way, HDS+HCI can in principle reach contrast limits of ~1e-5 x 1e-5, although in practice this will be limited by photon noise and/or sky-background. Methods: We present simulations of HDS+HCI observations with the E-ELT, both probing thermal emission from a planet at infrared wavelengths, and starlight reflected off a planet atmosphere at optical wavelengths. For the infrared simulations we use the baseline parameters of the E-ELT and METIS instrument, with the latter combining extreme adaptive optics with an R=100,000 IFS. We include realistic models of the adaptive optics performance and atmospheric transmission and emission. For the optical simulation we also assume R=100,000 IFS with adaptive optics capabilities at the E-ELT. Results: One night of HDS+HCI observations with the E-ELT at 4.8 um (d_lambda = 0.07 um) can detect a planet orbiting alpha Cen A with a radius of R=1.5 R_earth and a twin-Earth thermal spectrum of T_eq=300 K at a signal-to-noise (S/N) of 5. In the optical, with a Strehl ratio performance of 0.3, reflected light from an Earth-size planet in the habitable zone of Proxima Centauri can be detected at a S/N of 10 in the same time frame. Recently, first HDS+HCI observations have shown the potential of this technique by determining the spin-rotation of the young massive exoplanet beta Pictoris b. [abridged]
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