let 'x' be the number then the reciprocal of is 1/x

the difference of a number and 2 times its reciprocal is 7/3:

x - 2*(1/x) = 7/3 multiply both sides by 3x and simplify

3x^2 - 7x - 6 = 0

by solving the quadratic equation we find

x1 = -2/3

x2 = 3

the numbers are -2/3 and 3.