A Great Cannon or a Mortar (but not a volley Gun) which has been joined by a Master Engineer may re-roll either one Scatter dice or one Artillery dice per turn (not the roll to determine the distance bounced by a cannonball!). Note that if the Engineer uses his re-roll ability during the firing of the war machine he has joined, he will not he able to shoot with his own missile weapon in the same Shooting phase (he is too busy kicking the gunners around). Remember that you must fire all the weapons requiring you to guess the range before any normal shooting.
When firing his own missile weapon, an Engineer can always choose a different target from the one fired upon by the machine he has joined.