In this paper we propose exponential type nonlinearities in order to blindly separate instantaneous mixtures of signals with symmetric probability distributions. These nonlinear functions are applied only in a certain range around zero in order to ensure the stability of the separating algorithm. The proposed truncated nonlinearities neutralize the effect of outliers while the higher order terms inherently present in the exponential function result in fast convergence especially for signals with bounded support. By varying the truncation threshold, signals with both sub-Gaussian and super-Gaussian probability distributions can be separated. Furthermore, when the sources consist of signals with mixed kurtosis signs we propose to estimate the characteristic function online in order to classify the signals as sub-Gaussian or super-Gaussian and consequently choose an adequate value of the truncation threshold. Finally, some computer simulations are presented to demonstrate the superior performance of the proposed idea.