In this paper, we propose MMER, a novel Multimodal Multi-task learning approach for Speech Emotion Recognition. MMER leverages a novel multimodal network based on early-fusion and cross-modal self-attention between text and acoustic modalities and solves three novel auxiliary tasks for learning emotion recognition from spoken utterances. In practice, MMER outperforms all our baselines and achieves state-of-the-art performance on the IEMOCAP benchmark. Additionally, we conduct extensive ablation studies and results analysis to prove the effectiveness of our proposed approach.