Dear student first of all your question is a little wrong. -10+3 is not equal to 10-3.
-10+3 = 3-10
This is the original relation. It can be explained as,
-10+3 means we need to add -10 to 3. To add a negative number with a positive number, we subtract the small number from large number (here 10-3 = 7) and then give the sign of the large number to answer (i.e., here large number is 10( since 10>3) and its sign is -ve. So we give -ve sign for the obtained answer 7. So answer beome -7)
So as per the explanation,
-10+3 = -(10-3)
= -7
Also 3-10 =
{To subtract a large number from small number as here, we subtract large from small and give negative sign}
= -(10-3)
= -7
So -10+3 = 3-10.