Suppose the radii  of two circles are r1 and r2 in inches

now area of circle= (pi)*r^2

in the problem

pi(r1^2 - r2^2)=2300  --------------------------1

and r1-r2=10---------------------------------------2

now in equation 1

pi(r1+r2)(r1-r2)=2300

pi(r1+r2)*10=2300

r1+r2=230/pi-------------------------------------3

now add equation 2 and 3

r1-r2=10

r1+r2=230/pi

2r1=10+230/pi

r1=5+230/pi

substitute pi=22/7

r1= 5 + (230*7)/22

r1=(110 +1610)/22

r1=1720/22

r1=78.2

thus r2=78.2-10

r2=68.2

final answer

r1=78.2 inches

r2=68.2 inches