Let T and M be, respectively, the precursor time of a certain precursor and the magnitude of a forthcoming earthquake. Observations may lead to a relationship of T versus M in a form of log(T)=a+bM. In this study, we will explore the physical basis of the relationship. Based on the log(T)−M relationships of two different precursors, we propose a method to predict the magnitude and failure time of the forthcoming earthquake. A testing example based on the log(T)−M relationships of presiemic radon concentration anomalies and gamma-ray emission changes observed at respective monitoring stations in Taiwan is given in this study. Results strongly confirm a high possibility of predicting the magnitude and failure time of a forthcoming earthquake just from the observed occurrence times of two different precursors based on their log(T)−M relationships.