Energy, $E \propto F^a A^b T^c$. $[E] = [F^a][A^b][T^c]$. $[ML^2T^{-2}] = [MLT^{-2}]^a [LT^{-2}]^b [T]^c = [M^a L^{a+b} T^{-2a-2b+c}]$. Comparing dimensions on both sides: $a = 1$; $a+b = 2 \Rightarrow b = 1$; $-2 = -2a - 2b + c \Rightarrow -2 = -2 - 2 + c \Rightarrow c = 2$. Thus, $[E] = [FAT^2]$.