The Time Reversal (TR) method is a well-known technique employed for reconstruction of initial sources on inverse problems involving sound wave propagation, such as the inverse Thermoacoustic Tomography problem, where the data is acquired on the boundary of a given domain. In the case of smooth and variable sound speed, and finite observation times, G.Uhlmann and P. Stefanov developed a modification of TR that leads to an iterative reconstruction formula in the form of a Neumann series. It's been observed that when wave attenuation is considered, the straightforward extension of the TR method fails to converge unless the attenuation coefficients are assumed to be sufficiently small. In this talk, I will present a new version of the Time Reversal method that allows us to obtain a reconstruction formula for the inverse problem of Thermoacoustic Tomography in the presence of ultrasound attenuation modeled by an integro-differential operator.