set.seed(412)   # for reproducibility
m = 10^6
t = rnorm(m, 30, sqrt(10))
s = rnorm(m, 20, sqrt(5))
d = t - s
mean(d);  var(d)
[1] 9.99688     # aprx E(D) = 10
[1] 15.00828    # aprx Var(D) = 15
mean(d > 0);  mean(t > s)
[1] 0.995112    # aprx P(D > 0) = ??
[1] 0.995112    # another method for same