Ten times my age minus five times my brother's age is 100. Ten years ago square of my age plus the square of my brother's age was also 100. How old is my brother?

Now your brother is 16 and you are 18 :
1) 16×5=80;
18×10=180;
180-80=100.
Ten years ago your brother was 6 and you were 8:
2)8^2=64;
6^2=36;
64+36=100.
So your brother is 16 years old.