When saying 「これで」, you’re referring to the situation. If you think of で as a destination, then これで is where events have led up to “this” (how things are now). “With this” is a fair translation.
It is used when talking about how things will be, due to those events that led up to “this”. Imagine you hear someone say, “With this, we can win.” Even without knowing what they are talking about, you know there was something that took place, and “with this” thing, they will win something (in this example).
With は, you are making “with this” the topic, meaning you’re talking about the current state (what’s happened) leading to how things are going to be (what will happen).
In this sentence from the book, some ways you can translate 「これではどうしようもない」 include:
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“Under these circumstances, there’s nothing I can do.”
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“Because of this, there’s nothing I can do.”
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“This being the case, there’s nothing I can do.”
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“With the way things are, there’s nothing I can do.”
Note how これで is standing in for the situation at hand (stated in the prior sentence; what happened in the past), and is followed by what will happen due to how things now are (what will happen in the future).
Once you get used to it, you don’t have to think of it in detail. If you hear someone say, “I subscribed to WaniKani. With this, I can master kanji,” you don’t think through “with this” as meaning “the thing that happened in the past will result in such a future”. The meaning is simply understood. It’s a matter of getting used to what これで conveys, and if you see it often it’ll become instinct.