In quantitative photoacoustic tomography (QPAT) we aim at reconstructing physical parameters of biological tissues from measured acoustic data. We present here a reconstruction method for QPAT in non-scattering media that allows the simultaneous reconstruction of the ultrasound speed, the absorption coefficient and the Gr\"uneisen coefficient with differential data. We show some numerical simulations with synthetic data to demonstrate the performance of the method. This is a joint work with Alexander Mamonov.