Understanding the distinct neural signatures that differentiate memory encoding from retrieval remains a key challenge in cognitive neuroscience. This study applies machine learning to EEG data from the Penn Electrophysiology of Encoding and Retrieval Study (PEERS), involving 100 participants across over 400 sessions, to classify these cognitive states. We used Discrete Wavelet Transform (DWT) on EEG signals from six critical brain regions and evaluated seven machine learning models. Gradient Boosting emerged as the most effective classifier, achieving 81.97% accuracy and a 91.62% AUC. To interpret this performance, we applied Explainable AI (XAI) methods, specifically SHapley Additive exPlanations (SHAP). This analysis revealed that theta-band relative energy, especially in the Left and Right Anterior Superior (LAS/RAS) regions, was the most influential predictor. Low theta-band energy and RMS values were particularly indicative of encoding states. Topographic maps provided further validation, showing significant neural differences in anterior regions, notably within the theta range. However, the study is limited by the use of a fixed 2.5 s analysis window and demographic skew in the dataset, which may affect generalizability. Future work should address these issues through varied windowing strategies and more diverse populations. This study advances understanding of cognitive memory processes and supports the development of adaptive, memory-aware AI systems, contributing to both neuroscience and neurotechnology.