I think they are two very different applications. For bug tracking you might want to take a look at Bugzilla. It is free and fairly complete. It is designed for software development bug tracking, I do not know if your engineering bug tracking would be much different but the source if available so it is also modifiable. The web site is:

http://www.bugzilla.org/.

As for help desk, there is such a wide range of products and you haven't provided much in the way of function requirements. We use CA's AHD here. It is a MONSTER and VERY expensive. There are also some very low end/shareware stuff. Here is a sample of a low end Help Desk:

http://www.dbandsons.com/OurSoftware.../Default.aspx.

I even wrote my own a couple of years ago that was used at a couple of hospitals for a while. But they eventually needed something a little more robust.

Just some thoughts...