We describe a monaural speech enhancement algorithm based on modulation-domain Kalman filtering to blindly track the time-frequency log-magnitude spectra of speech and reverberation. We propose an adaptive algorithm that performs blind joint denoising and dereverberation, while accounting for the inter-frame speech dynamics, by estimating the posterior distribution of the speech log-magnitude spectrum given the log-magnitude spectrum of the noisy reverberant speech. The Kalman filter update step models the non-linear relations between the speech, noise and reverberation log-spectra. The Kalman filtering algorithm uses a signal model that takes into account the reverberation parameters of the reverberation time, $T_{60}$, and the direct-to-reverberant energy ratio (DRR) and also estimates and tracks the $T_{60}$ and the DRR in every frequency bin in order to improve the estimation of the speech log-magnitude spectrum. The Kalman filtering algorithm is tested and graphs that depict the estimated reverberation features over time are examined. The proposed algorithm is evaluated in terms of speech quality, speech intelligibility and dereverberation performance for a range of reverberation parameters and SNRs, in different noise types, and is also compared to competing denoising and dereverberation techniques. Experimental results using noisy reverberant speech demonstrate the effectiveness of the enhancement algorithm.