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After learning some basic abstract algebra I found out that it's important to mention from which side we perform an operation on both sides of an equation. Not all operations are commutative.
For operations like multiplication it doesn't matter from which side we do it (because it's commutative), but for operations like subtraction, which is not commutative, we should probably specify that we subtract from the right. Alternatively we could say "add -x to both sides of the equation" because addition is commutative.

What do you think?

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    Why say extra words if everyone understands what you mean with less verbosity? But yes, technically the subtraction should be done from the right on both sides (though if you instead subtracted both sides from the number on the right instead, you'd get an equivalent equation). – 2017-02-25
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    "subtract $x$" is something that does not matter which side you do it on, so there is no need to specify one. – 2017-02-25
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    Multiplication of matrices is generally not commutative, so in that case you have to specify what side it is being done on. I think what you are raising, subtraction of numbers, is a non-issue because "subtract $x$" *means* adding $-x$ and thus order does not matter: $a - x = -x + a$. It is like asking if we need to be careful when saying "divide by $x$" because division is not commutative. This too is not problematic because that phrase *means* multiplying by $1/x$: $a/x = (1/x)a$. I think you are posing a solution in search of a problem. – 2017-02-25

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It's implied by the grammar and word order in the sentence.

"Subtract $x$ from $y$" always means $y-x$. So if you have an equation $y=z$, then "subtract $x$ from both sides" unambiguously means $y-x = z-x$.

If you wanted $x-y = x-z$, you would say "Subtract both sides from $x$".