Linda thinks of a two digit number. the sum of the digits is 8. if she reverses the digits, the new number is 26 greater than her original number.

Let
x = the 10s digit
y = the units
N1> original number
N2> new number
N2=N1+36 >N2-N1=36
y+x=8 > equation (I)
then
10x + y = N1
10y+x=N2

(10y+x)-(10x+y)=36- > 9y-9x=36 > y-x=4 > equation (II)

resolving (I) and (II)
 y+x=8
 y- x=4

2y+0x=12 >y=6
then
x=8-y=8-6=2> x=2

N1=26 and N2=62

the two digit number is 26