As enterprise information systems are collecting event streams from various sources, the ability of a system to automatically detect anomalous events and further provide human-readable explanations is of paramount importance. In this paper, we present an approach to integrated anomaly detection (AD) and explanation discovery (ED), which is able to leverage state-of-the-art Deep Learning (DL) techniques for anomaly detection, while being able to recover human-readable explanations for detected anomalies. At the core of the framework is a new human-interpretable dimensionality reduction (HIDR) method that not only reduces the dimensionality of the data, but also maintains a meaningful mapping from the original features to the transformed low-dimensional features. Such transformed features can be fed into any DL technique designed for anomaly detection, and the feature mapping will be used to recover human-readable explanations through a suite of new feature selection and explanation discovery methods. Evaluation using a recent explainable anomaly detection benchmark demonstrates the efficiency and effectiveness of HIDR for AD, and the result that while all three recent ED techniques failed to generate quality explanations on high-dimensional data, our HIDR-based ED framework can enable them to generate explanations with dramatic improvements in the quality of explanations and computational efficiency.