Visible and near-infrared spectra of transiting hot Jupiter planets have recently been observed, revealing some of the atmospheric constituents of their atmospheres. In the near future, it is probable that primary and secondary eclipse observations of Earth-like rocky planets will also be achieved. The characterization of Earth's transmission spectrum has shown that both major and trace atmospheric constituents may present strong absorption features, including important bio-markers such as water, oxygen, and methane. Our simulations using a recently published empirical Earth's transmission spectrum, and the stellar spectra for a variety of stellar types, indicate that the new generation of extremely large telescopes, such as the proposed 42 m European Extremely Large Telescope, could be capable of retrieving the transmission spectrum of an Earth-like planet around very cool stars and brown dwarfs (T eff <= ~3100 K). For a twin of Earth around a star with T eff ~ 3100 K (M4), for example, the spectral features of H2O, CH4, CO2, and O2 in the wavelength range between 0.9 and 2.4 μm can simultaneously be detected within 100 hr of observing time, or even less for a late-M star. Such detection would constitute proof for the existence of life in that planet. The detection time can be reduced to a few hours for a super-Earth type of planet with twice Earth's radius.