Search systems control the exposure of ranked content to searchers. In many cases, creators value not only the exposure of their content but, moreover, an understanding of the specific searches where the content is surfaced. The problem of identifying which queries expose a given piece of content in the ranking results is an important and relatively under-explored search transparency challenge. Exposing queries are useful for quantifying various issues of search bias, privacy, data protection, security, and search engine optimization. Exact identification of exposing queries in a given system is computationally expensive, especially in dynamic contexts such as web search. In quest of a more lightweight solution, we explore the feasibility of approximate exposing query identification (EQI) as a retrieval task by reversing the role of queries and documents in two classes of search systems: dense dual-encoder models and traditional BM25 models. We then propose how this approach can be improved through metric learning over the retrieval embedding space. We further derive an evaluation metric to measure the quality of a ranking of exposing queries, as well as conducting an empirical analysis focusing on various practical aspects of approximate EQI.