Call the missing numbers A, B, C, D from left to right, top to bottom.
A+5+B=33+C+49=D+77+19=A+33+D=5+C+77=B+49+19=A+C+19=B+C+D.
A+B+5=C+82=D+96=A+D+33=B+68=A+C+19=B+C+D.
D+96=A+D+33, 96=A+33, A=63. Replace A in other expressions and rewrite the list, omitting duplicates:
B+68=C+82=D+96=B+C+D. C+D=68 and C-D=14, so, adding, 2C=82, C=41. So, D=27.
B+68=41+82, so B=55. The common sum is 123.
63 |
5 |
55 |
33 |
41 |
49 |
27 |
77 |
19 |