A x 4 = E B ÷ 4 = E C + 4 = E D - 4 = E ___________ & A + B + C + D = 100 Challenge *what?

This is called substitution. You are given:
A = E/4
B = 4E
C = E - 4
D = E + 4

So substitute those into the challenge:

E/4 + 4E + E - 4 + E + 4 = 100

and do the arithmetic.