Current abstractive summarization systems outperform their extractive counterparts, but their widespread adoption is inhibited by the inherent lack of interpretability. To achieve the best of both worlds, we propose EASE, an extractive-abstractive framework for evidence-based text generation and apply it to document summarization. We present an explainable summarization system based on the Information Bottleneck principle that is jointly trained for extraction and abstraction in an end-to-end fashion. Inspired by previous research that humans use a two-stage framework to summarize long documents (Jing and McKeown, 2000), our framework first extracts a pre-defined amount of evidence spans as explanations and then generates a summary using only the evidence. Using automatic and human evaluations, we show that explanations from our framework are more relevant than simple baselines, without substantially sacrificing the quality of the generated summary.