Biomedical photoacoustic tomography (PAT), as a future imaging modality, can visualize the internal structure and function of soft tissues with high spatial resolution and excellent optical contrast as well as satisfactory imaging depth. A key issue for this unique imaging technique is to recover both the optical absorption and scattering coefficients from the measured acoustic data. Previous attempts in quantitative PAT(qPAT) have been implemented to deduce the map of absorption coefficient from the absorbed energy density using either a model-based method or the invasive measurement techniques when an assumed scattering coefficient is used. However, optical scattering in biological tissue typically dominates over absorption by an order of magnitude or more. Due to this effect it is very challenging to image tissues with highly scattering and accurately recover the absorption coefficient photoacoustically. In this study we propose and validate by experiment tests that quantitative scattering map can be recovered using the measured acoustic data from one-wavelength illumination. The developed reconstruction algorithm relies on PAT and coupled diffusion equation to recover the optical absorption coefficient and energy density, and the diffusion model only to recover the optical scattering coefficients. In particular, this algorithm has the capability to resolve the crosstalk issue in diffuse optical tomography (DOT) and achieve high resolution DOT using acoustics measurements.