Right i just solved this to get the general solution, but i'm not sure it's right.
assumption 1: he calls a 3flush river with the same frequency that he calls my shove on the turn. (not true but massively simplifying)
assumption 2: i can't win the hand unless i hit a flush.
assumption 3: i never bluff the river if i miss (not true lol).
if someone could check this i'd be very happy..
x = calling frequency
EV of checking = [0.2((x*$10)+$15)] = 2x + 3
EV of shoving = x[(0.2*$35)-$10] + (1-x)*$15 = -3x + 15 - 15x
EV of shoving = 5 - 6x
grapically:
this suggests that shoving and checking have equal value at a calling frequency of 25% - if he calls more than that and checking has more value.
the thing that concerns me is that shoving is profitable until he calls 85% of the time. if someone could check this using whatever method they normally use to check FE that would be really awesome.