Well done, nacw, with thanks also to geevo & emmie.
To locate 'augment', most of the 7-letter possibilities can be discarded for one reason or another, leaving just two 'possibles'. These have 17 and 9 for E. 9 appears just before a given C at the end of a word, which is almost never anything but an I. Hence I worked on the basis that E = 17.