In this paper, for real time enhancement of noisy speech, a method of threshold determination based on modeling of Teager energy (TE) operated perceptual wavelet packet (PWP) coefficients of the noisy speech and noise by an Erlang-2 PDF is presented. The proposed method is computationally much faster than the existing wavelet packet based thresholding methods. A custom thresholding function based on a combination of mu-law and semisoft thresholding functions is designed and exploited to apply the statistically derived threshold upon the PWP coefficients. The proposed custom thresholding function works as a mu-law or a semisoft thresholding function or their combination based on the probability of speech presence and absence in a subband of the PWP transformed noisy speech. By using the speech files available in NOIZEUS database, a number of simulations are performed to evaluate the performance of the proposed method for speech signals in the presence of Gaussian white and street noises. The proposed method outperforms some of the state-of-the-art speech enhancement methods both at high and low levels of SNRs in terms of standard objective measures and subjective evaluations including formal listening tests.