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 I will 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. I will 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, I will demonstrate its application using the N=4 Supersymmetric Yang-Mills theory as an example. Additionally, I will touch upon the potential generalization of this approach to QCD.