The 3 corners get counted twice so they should have the highest numbers: 9, 8, 7

9 should get the 2 smallest numbers in it's 2 sides: 1, 2

We now have 9+1=10 & 9+2=11 add 7 and 8, must be 17 and 19 (18 and 18 won't work)
The numbers left are 3, 4, 5, 6
Either 5 and 3 or 6 and 4 go with the 17 and 19 = either 22 ( 5 and 3) or 23 (6 and 4)
The remaining side has 7 and 8 for 15. Add the 2 remaining number and get either 15 + 8 = 23
or 15 + 10 = 25
So the total that matches is 23 as the highest possible equal total.
9 1 6 7
,2 , , 5
,,4 3
,,,8