To find the distance between two points \( E(10, -2) \) and \( F(-2, 3) \) in a 2-dimensional plane, we use the distance formula given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here, \( (x_1, y_1) \) is the coordinates of point E and \( (x_2, y_2) \) is the coordinates of point F:
- \( E(10, -2) \): \( x_1 = 10 \) and \( y_1 = -2 \)
- \( F(-2, 3) \): \( x_2 = -2 \) and \( y_2 = 3 \)
Now, we can plug the values into the distance formula:
\[ d = \sqrt{((-2) - 10)^2 + (3 - (-2))^2} \]
Calculating the differences:
\[ d = \sqrt{(-12)^2 + (5)^2} \]
Calculating the squares:
\[ d = \sqrt{144 + 25} \]
Now, add the results:
\[ d = \sqrt{169} \]
Taking the square root:
\[ d = 13 \]
Thus, the distance between the points \( E \) and \( F \) is:
\[ \boxed{13} \]