let 'x', 'y' and 'z' bu the numbers

the sum of three numbers is 26

x + y + z = 26

twice the first minus the second is 2 less than the third

2x - y = z - 2

the third is the second minus three times the first

z = y - 3x

by solving the system of equations

x + y + z = 26

2x - y = z - 2

z = y - 3x

we get

x = 8

y = 21

z = -3

the numbers are 8, 21 and -3.