  We present a new method to retrieve molecular abundances and temperature
profiles from exoplanet atmosphere photometry and spectroscopy. We run millions
of 1D atmosphere models in order to cover the large range of allowed parameter
space, and present error contours in the atmospheric properties, given the
data. In order to run such a large number of models, we have developed a
parametric pressure-temperature (P-T) profile coupled with line-by-line
radiative transfer, hydrostatic equilibrium, and energy balance, along with
prescriptions for non-equilibrium molecular composition and energy
redistribution. We apply our temperature and abundance retrieval method to the
atmospheres of two transiting exoplanets, HD 189733b and HD 209458b, which have
the best available Spitzer and HST observations. For HD 189733b, we find
efficient day-night redistribution of energy in the atmosphere, and molecular
abundance constraints confirming the presence of H2O, CO, CH4, and CO2. For HD
209458b, we confirm and constrain the day-side thermal inversion in an average
1D temperature profile. We also report independent detections of H$_2$O, CO,
CH$_4$ and CO$_2$ on the dayside of HD 209458b, based on six-channel Spitzer
photometry. We report constraints for HD 189733b due to individual data sets
separately; a few key observations are variable in different data sets at
similar wavelengths. Moreover, a noticeably strong carbon dioxide absorption in
one data set is significantly weaker in another. We must, therefore,
acknowledge the strong possibility that the atmosphere is variable, both in its
energy redistribution state and in the chemical abundances.
