We first consider the inverse problem of identifying the distribution of fluorophores in biological tissue from the time domain measurement on the boundary. With the Laplace transform and the knowledge of complex analysis, we build the uniqueness theorem of this inverse problem. Further, we consider a simultaneous inverse problem in the time-domain diffuse optical tomography with fluorescence. Under a special setup of boundary input, we build the uniqueness of this simultaneous inverse problem. After that, the numerical inversions are considered. We introduce an iterative inversion algorithm under the framework of regularizing scheme, then give several numerical examples illustrating the performance of the proposed inversion schemes.