You can use either: one from the other the one from the other Both are OK.

This is because "one" is not specific, and "the one" is specific. That is, when you say "one from the other" you mean that you cannot tell the difference between ANY two umbrellas in the group. This most likely means there are more than two umbrellas. If you say "the one from the other" is more specific. It sounds as if you are speaking about only two umbrellas; that is, "the one" and "the other". However if you are only speaking about two umbrellas, you could certainly use "the one from the other".

”the”あるの時、”the one”は”特別”の意味をある。例の意味の中でその傘は”特別”ではありわせん。”one”は十分だ。