Text summarization is a natural language processing method that reduces the text in the article and provides the important information from the document. Few researches have been carried out in the text summarization in the Telugu language and have lower efficiency in Telugu Text summarization. In this research, the Long-Short Term Memory (LSTM) with Rectified Adam Optimizer (RAdam) method and focal loss function is proposed for text summarization in Telugu e-news data. The Eenadu Telugu e-news data of various categories are collected to evaluate the performance of the proposed LSTM with RAdam method. Tokenization method is applied in the pre-processing method to extract the important keywords from the input data. Focal loss function is applied between the cells of LSTM to handle the imbalance data problem. Modulation function in the focal loss function down weight the easy examples to focus on hard examples and effectively handles the imbalance data. The proposed LSTM with RAdam method has advantage of using Exponential Moving Average (EMA) for adaptive learning rate and rectify the variance. The proposed LSTM with RAdam method is evaluated in 10 categories of e-news data to analysis the performance. This proposed LSTM with RAdam method has 93.46% accuracy and existing LSTM method has 86.92% accuracy.