In open question answering (QA), the answer to a question is produced by retrieving and then analyzing documents that might contain answers to the question. Most open QA systems have considered only retrieving information from unstructured text. Here we consider for the first time open QA over {\em both} tabular and textual data and present a new large-scale dataset \emph{Open Table-and-Text Question Answering} (OTT-QA) to evaluate performance on this task. Most questions in OTT-QA require multi-hop inference across tabular data and unstructured text, and the evidence required to answer a question can be distributed in different ways over these two types of input, making evidence retrieval challenging---our baseline model using an iterative retriever and BERT-based reader achieves an exact match score less than 10\%. We then propose two novel techniques to address the challenge of retrieving and aggregating evidence for OTT-QA. The first technique is to use ``early fusion'' to group multiple highly relevant tabular and textual units into a fused block, which provides more context for the retriever to search for. The second technique is to use a cross-block reader to model the cross-dependency between multiple retrieved evidence with global-local sparse attention. Combining these two techniques improves the score significantly, to above 27\%.