Engineers work out showing determination (7)
I believe the answer is:
resolve
'determination' is the definition.
(I've seen this before)
'engineers work out' is the wordplay.
'engineers' becomes 're' (Royal Engineers).
'work out' becomes 'solve' (I've seen this in another clue).
're'+'solve'='RESOLVE'
'showing' acts as a link.
(Other definitions for resolve that I've seen before include "work out" , "Settle; firmness of intent" , "Find the solution (to)" , "Determine with conviction" , "Decide; firm determination" .)