This is a new lifetime Exponential "distribution using the Topp-Leone generated family of distributions proposed by Rezaei et al. The new distribution is called the Topp-Leone Exponential (TLE) distribution". What is done in this paper is an estimation of the "unlabeled two parameters for Topp-Leone Exponential distribution model by using the maximum likelihood estimator method to get the derivation of the point estimators for all unlabeled parameters according to iterative techniques as Newton $-$ Raphson method, then to derive Ordinary least squares estimator method". "Applying all two methods to estimate related probability functions; death density function, cumulative distribution function, survival function and hazard function (rate function)". When examining the numerical results for probability survival function by employing mean squares error measure and mean absolute percentage measure, this may lead to work on the best method in modeling a set of real data.