Letter Land

We can simplify most of these equations first, before we start giving values to all of the letters.

As $A + C = A$ we know that $C = 0$.

As $F \times D = F$ we know that $D = 1$.

$B - G = G$, therefore $B = 2G$ (add $G$ to both sides of the equation).
$B / H = G$ therefore $B = HG$ (multiply both sides by $H$).

Since $B = HG$, and $B$ also equals $2G$,
$H$ must be $2$.

Since $B$ is twice $G$, the options are:

So $B = 6$ and $G = 3$

$E - G = F$, therefore $E - 3 = F$.
The smallest possible value for $F$ is $4$, and this means that $E$ would be $7$.
$F$ cannot be any greater than $4$ because this would mean that $E > 7$ and this is not allowed.
Therefore $F = 4$ and $E = 7$

Now we can solve $A + H = E$.
This is $A + 2 = 7$, so $A = 5$.

Here are the solved equations:

And all the values of $A$-$H$: