Energy-Energy Correlation (EEC) measures the energy-weighted angular correlation of pair of particles in e+e- collisions. In the back-to-back limit, EEC exhibits typical Sudakov double logarithms that can be resummed using standard TMD factorization formula. In this talk we present a new approach to the resummation of Sudakov double logarithms for EEC, which involves the utilization of a local operator product expansion, conformal block, and large spin summation. We show that classical conformal symmetry of massless QCD lagrangian can be used to resummed certain power corrections in the back-to-back region. To illustrate the effectiveness of this approach, We demonstrate its application using the N=4 Supersymmetric Yang-Mills theory as an example. Generalization to the QCD case will be briefly discussed.