This study investigates the time-scale dependence between the Nifty Energy Index and the Nifty ESG Index using wavelet analysis, utilizing daily return data from December 30, 2016, to February 7, 2025, we apply Wavelet Coherence Analysis (WTC) to examine co-movement patterns across different investment horizons. The findings reveal that the correlation between energy and ESG investments varies over time, with the strongest coherence observed at 8-day and 64-day intervals, short-term market reactions and medium-term financial trends. While ESG and energy indices exhibit moderate long-term alignment. The study contributes to sustainable finance literature by demonstrating how wavelet-based techniques can enhance understanding of ESG-Energy interactions, offering valuable implications for investors, policymakers, and portfolio managers seeking to optimize ESG-integrated investment strategies.