let

x = the first number

y = the second number

z = the third number

the sum of three numbers is 18

x + y + z = 18

the sum of twice the first number, and 4 times the third number is 52

2x +4z = 52

the difference between 7 times the first number and the second number is 43

7x - y = 43

by solving the system of equations

x + y + z = 18

2x +4z = 52

7x - y = 43

we find

x = 6.4

y = 1.8

z = 9.8

the three numbers are 6.4, 1.8 and 9.8.