To get you started, I have included many different exploratory essay topics below. For many of the topics, I've included one or more links to essays which will get you thinking about the topic. Some of these essays are also found in the college English textbook that I use with my students, Perspectives on Argument by Nancy Wood.
Writing the Exploratory essay is something new and unusual to you. This kind of papers is the opposite side of the papers that you have written before. When choosing the topic of the exploratory essay you do not have to be familiar or well-educated on the question you are talking about. The main purpose of the exploratory essay is to learn in the process of writing and researching. And you don’t have to prove that you know something about the topic at the very beginning of the exploratory essay topic.
100 Exploratory Essay Topic Ideas | LetterPile
If you are not able to pick your own Exploratory essays topics, then you will have to stick to what your teacher/professor makes you write about. This is bad because you are most probably is not keen to learn about this particular Research essay topic. However, the positive moment is that if the Exploratory type essay is based on something that the school syllabus demands, then there is a very good chance to find some first class help.