Sentiment analysis is often used to examine how different actors are portrayed in the media, and analysis of news headlines is of particular interest due to their attention-grabbing role. We address the task of entity-level sentiment analysis from Croatian news headlines. We frame the task as targeted sentiment analysis (TSA), explicitly differentiating between sentiment toward a named entity and the overall tone of the headline. We describe SToNe, a new dataset for this task with sentiment and tone labels. We implement several neural benchmark models, utilizing single- and multi-task training, and show that TSA can benefit from tone information. Finally, we gauge the difficulty of this task by leveraging dataset cartography.