Faith versus works

I remember being taught Fielding's Joseph Andrews for A-level (back in the way back when) as, in large part, a comic-satiric intervention into eighteenth-century theological debates as to whether justification is by faith or works. At the time it seemed a more-or-less abstruse question, in part because good works struck my teenage mind as so obviously a better way to live your life than intense faith (a position, of course, that had nothing to do with scripture). From time to time I am surprised by how vigorously this problematic can manifest itself. It is, for instance, behind Eliot's Becket:

Now is my way clear, now is the meaning plain:
Temptation shall not come in this kind again.
The last temptation is the greatest treason:
To do the right deed for the wrong reason.

I honestly don't see that the hyperbole of 'greatest treason' can be understood out of the context of this debate.

But coming back to it again, what once seemed to me not only clear cut but straightforward strikes me now as immensely complicated and even incoherent. What is the distinction between drawn between 'faith' and 'works'? How can faith not be a 'work', and how can any works be undertaken not motivated by faith? Aren't these things, actually, the same thing -- not in the shallow sense (behind Becket's words, perhaps) that 'faith' means 'a reason for acting in a certain way', but in the deeper sense that our various internal forces of faith situate and position our being-in-the-world?