To ensure the safety and reliability of an echelon-use lithium-ion battery (EULIB), the performance of a EULIB is accurately reflected. This paper presents a method of estimating the combined state of energy (SOE) and state of charge (SOC). First, aiming to improve the accuracy of the SOE and SOC estimation, a third-order resistor-capacitance equivalent model (TRCEM) of a EULIB is established. Second, long short-term memory (LSTM) is introduced to optimize the Ohmic internal resistance (OIR), actual energy (AE), and actual capacity (AC) parameters in real time to improve the accuracy of the model. Third, in the process of the SOE and SOC estimation, the observation noise equation and process noise equation are updated iteratively to make adaptive corrections and enhance the adaptive ability. Finally, an SOE and SOC estimation method based on LSTM optimization and an adaptive extended Kalman filter (AEKF) is established. In simulation experiments, when the capacity decays to 90%, 60% and 30% of the rated capacity, regardless of whether the initial value is consistent with the actual value, the values of the SOE and SOC estimation can track the actual value with strong adaptive ability, and the estimated error is less than 1.19%, indicating that the algorithm has a high level of accuracy. The method presented in this paper provides a new perspective for estimating the SOE and SOC of a EULIB.