Sure, typing an essay seems like a simple problem at first, and it is if you do it on a typewriter. A problem I've noticed many times before came to light yet again when I was preparing the overheads for my CVS presentation. I wanted to start with my content, but had to pay attention to formatting from the very beginning. MS Word's style sheet system, which is actually quite nice, between the DOS and Windows versions of Word somehow got buried beneath layers of other stuff. I think that these two points demonstrate the two branches of the complexity problem we're dealing with.
Essential complexity is that that is part of the problem itself.
Accidental complexity is additional complexity that has been introduced into the problem, usually as part of the process of solving it. Accidental complexity can be reduced without affecting the solution of the problem itself. Fred Brooks applies this to software development, but I think this applies equally to my experience with MS word. In point one above, I had my mind full of the content of my overhead slides, not the presentation. I knew that a particular sentence I was typing would be a header, or a bullet point, or a code example, but I didn't care what it looked like at the time, so long as I could read it.