The paper reports an exact solution for spectral profiles of time-resolved fluorescence following a broad-band excitation producing changes in both the chromophore's dipole moment and the polarizability. The problem is formulated in terms of a two-state chromophore with a bilinear coupling to a Gaussian solvent mode. Closed-form solutions for the time-dependent spectral shift and width are obtained. These two transient spectral moments are sufficient to generate transient, non-Gaussian band-shapes by using the proposed formalism. An approximately linear relation between the normalized shift and width time correlation functions is found. The Stokes shift correlation function is virtually insensitive to the nonlinear solute-solvent effects, in spite of dramatic transient changes in the spectral width. Depending on chromophore's parameters, the transient line shape can be well approximated by a nonstationary Gaussian process or shows clearly non-Gaussian statistics. The model is extended to treat heterogeneous solvent dynamics.