While the importance of "expressive writing," or informal, self-directed writing, has been well established, teachers underutilize it, particularly in technical writing courses. We introduce the term expressive/exploratory technical writing (XTW), which is the use of informal, self-directed writing to problem-solve in technical fields. We describe how engineering students resist writing, despite decades of research showing its importance to their careers, and we suggest that such resistance may be because most students only see writing as an audience-driven performance and thus incompletely understand the link between writing and thinking. The treatment of invention in rhetorical history supports their view. We describe two examples of using XTW in software engineering to plan programming tasks. We conclude by discussing how a systematic use of XTW could shift the technical writing curriculum, imbuing the curriculum with writing and helping students see how to problem-solve using natural language.