Long-Term Evolution in the unlicensed spectrum (LTE-U) is considered as an indispensable technique to mitigate the spectrum scarcity in wireless networks. Typical LTE transmissions are contention-free and centrally controlled by the base station (BS); however, the wireless networks that work in unlicensed bands use contention-based protocols for channel access, which raises the need to derive an efficient and fair coexistence mechanism among different radio access networks. In this work, we propose a novel neural networks (NNs) based mechanism for the coexistence of an LTE-U base station (BS) in the unlicensed spectrum alongside with a WiFi access point (WAP). Specifically, we model the coexistence problem as a Hopfield Neural Network (HNN) based optimization problem that aims a fair coexistence considering both the LTE-U data rate and the QoS requirements of the WiFi network. Using the energy function of HNN, precise investigation of its minimization property can directly provide the solution of the optimization problem. Numerical results show that the proposed mechanism allows the LTE-U BS to work efficiently in the unlicensed spectrum while protecting the WiFi network.