Price forecasting is at the center of decision making in electricity markets. Much research has been done in forecasting energy prices for a single market while little research has been reported on forecasting price difference between markets, which presents higher volatility and yet plays a critical role in applications such as virtual trading. To this end, this paper takes the first attempt at it and employs novel deep learning architecture with Bidirectional Long-Short Term Memory (LSTM) units and Sequence-to-Sequence (Seq2Seq) architecture to forecast nodal price difference between day-ahead and real-time markets. In addition to value prediction, these deep learning architectures are also used to develop classification models to predict the price difference bands/ranges. The proposed methods are tested using historical PJM market data, and evaluated using Root Mean Squared Error (RMSE) and other customized performance metrics. Case studies show that both deep learning methods outperform common methods including ARIMA, XGBoost and Support Vector Regression (SVR) methods. More importantly, the deep learning methods can capture the magnitude and timing of price difference spikes. Numerical results show the Seq2Seq model performs particularly well and demonstrates generalization capability to extended forecasting lead time.