This paper introduces RTEx, a novel methodology for a) ranking radiography exams based on their probability to contain an abnormality, b) generating abnormality tags for abnormal exams, and c) providing a diagnostic explanation in natural language for each abnormal exam. The task of ranking radiography exams is an important first step for practitioners who want to identify and prioritize those radiography exams that are more likely to contain abnormalities, for example, to avoid mistakes due to tiredness or to manage heavy workload (e.g., during a pandemic). We used two publicly available datasets to assess our methodology and demonstrate that for the task of ranking it outperforms its competitors in terms of NDCG@k. For each abnormal radiography exam RTEx generates a set of abnormality tags alongside an explanatory diagnostic text to explain the tags and guide the medical expert. Our tagging component outperforms two strong competitor methods in terms of F1. Moreover, the diagnostic captioning component of RTEx, which exploits the already extracted tags to constrain the captioning process, outperforms all competitors with respect to clinical precision and recall.