Purpose: Echo modulation curve (EMC) modeling can provide accurate and reproducible quantification of T2 relaxation times. The standard EMC-T2 mapping framework, however, requires sufficient echoes and cumbersome pixel-wise dictionary-matching steps. This work proposes a deep learning version of EMC-T2 mapping, called DeepEMC-T2 mapping, to efficiently estimate accurate T2 maps from fewer echoes without a dictionary. Methods: DeepEMC-T2 mapping was developed using a modified U-Net to estimate both T2 and Proton Density (PD) maps directly from multi-echo spin-echo (MESE) images. The modified U-Net employs several new features to improve the accuracy of T2/PD estimation. MESE datasets from 68 subjects were used for training and evaluation of the DeepEMC-T2 mapping technique. Multiple experiments were conducted to evaluate the impact of the proposed new features on DeepEMC-T2 mapping. Results: DeepEMC-T2 mapping achieved T2 estimation errors ranging from 3%-12% in different T2 ranges and 0.8%-1.7% for PD estimation with 10/7/5/3 echoes, which yielded more accurate parameter estimation than standard EMC-T2 mapping. The new features proposed in DeepEMC-T2 mapping enabled improved parameter estimation. The use of a larger echo spacing with fewer echoes can maintain the accuracy of T2 and PD estimations while reducing the number of 180-degree refocusing pulses. Conclusions: DeepEMC-T2 mapping enables simplified, efficient, and accurate T2 quantification directly from MESE images without a time-consuming dictionary-matching step and requires fewer echoes. This allows for increased volumetric coverage and/or decreased SAR by reducing the number of 180-degree refocusing pulses.