In this paper, an end-to-end neural embedding system based on triplet loss and residual learning has been proposed for speech emotion recognition. The proposed system learns the embeddings from the emotional information of the speech utterances. The learned embeddings are used to recognize the emotions portrayed by given speech samples of various lengths. The proposed system implements Residual Neural Network architecture. It is trained using softmax pre-training and triplet loss function. The weights between the fully connected and embedding layers of the trained network are used to calculate the embedding values. The embedding representations of various emotions are mapped onto a hyperplane, and the angles among them are computed using the cosine similarity. These angles are utilized to classify a new speech sample into its appropriate emotion class. The proposed system has demonstrated 91.67\% and 64.44\% accuracy while recognizing emotions for RAVDESS and IEMOCAP dataset, respectively.