Non-native speakers with limited vocabulary often struggle to name specific objects despite being able to visualize them, e.g., people outside Australia searching for numbats. Further, users may want to search for such elusive objects with difficult-to-sketch interactions, e.g., numbat digging in the ground. In such common but complex situations, users desire a search interface that accepts composite multimodal queries comprising hand-drawn sketches of difficult-to-name but easy-to-draw objects and text describing difficult-to-sketch but easy-to-verbalize object attributes or interaction with the scene. This novel problem statement distinctly differs from the previously well-researched TBIR (text-based image retrieval) and SBIR (sketch-based image retrieval) problems. To study this under-explored task, we curate a dataset, CSTBIR (Composite Sketch+Text Based Image Retrieval), consisting of approx. 2M queries and 108K natural scene images. Further, as a solution to this problem, we propose a pretrained multimodal transformer-based baseline, STNET (Sketch+Text Network), that uses a hand-drawn sketch to localize relevant objects in the natural scene image, and encodes the text and image to perform image retrieval. In addition to contrastive learning, we propose multiple training objectives that improve the performance of our model. Extensive experiments show that our proposed method outperforms several state-of-the-art retrieval methods for text-only, sketch-only, and composite query modalities. We make the dataset and code available at our project website.