A novel approach to distributed fiber-optic Brillouin sensing is presented and numerically analyzed. An integral equation that directly relates the Brillouin gain to the Brillouin signal is derived in the frequency domain, and from this result a new technique for the quantitative reconstruction of temperature-strain profiles along an optical fiber is developed. We achieve the reconstruction by minimizing a cost function that represents the error between the measured and the model data. We effectively perform such a minimization by representing the unknown (temperature-strain) profile with a finite number of parameters. Numerical results confirm the effectiveness of the proposed approach and its stability against noise in the data.