Let 1st number be: X

let 2nd number be: Y

let the minimum be: M

1 x-y=16 --> x=16+y

2 m=x+y+xy

sub 1 into 2

m=(16+y)+y+(16+y)y

=y^2+18y+16

y^2+18y+81-81+16

m=(y+9)^2-65

therefore y=-9

sub y=-9 into 1

x=16+(-9)

x=7

therefore the first number is 7 and the second is -9

let 2nd number be: Y

let the minimum be: M

1 x-y=16 --> x=16+y

2 m=x+y+xy

sub 1 into 2

m=(16+y)+y+(16+y)y

=y^2+18y+16

y^2+18y+81-81+16

m=(y+9)^2-65

therefore y=-9

sub y=-9 into 1

x=16+(-9)

x=7

therefore the first number is 7 and the second is -9