Would killing one be in line with EA if it can save 10?

A short answer might be "In real life, people view these two scenarios very differently, and ignoring psychology and sociology may get you some interesting thought experiments but will not lead you anywhere useful when working with actual humans."

Or to quote the EA Guiding Principles:

"Because we believe that trust, cooperation, and accurate information are essential to doing good, we strive to be honest and trustworthy. More broadly, we strive to follow those rules of good conduct that allow communities (and the people within them) to thrive." Not killing people seems like a pretty basic requirement for trust and cooperation. There are socially-agreed-upon exceptions like governments having use of force, but even those are divisive.

Some other writing that's addressed this:

https://www.lesswrong.com/posts/prb8raC4XGJiRWs5n/consequentialism-need-not-be-nearsighted

https://www.lesswrong.com/posts/K9ZaZXDnL3SEmYZqB/ends-don-t-justify-means-among-humans

Here are two other considerations that haven't yet been mentioned:

1. EA is supposed to be largely neutral between ethical theories. In practice, most EAs tend to be consequentialists, specifically utilitarians, and a utilitarian might plausibly think that killing one to save ten was the right thing to do (though others in this thread have given reasons why that might not be the case even under utilitarianism), but in theory one could unite EA principles with most ethical systems. So if the ethical system you think is most likely to be correct includes side constraints/deontological rules against killing, then EA doesn't require you to violate those side constraints in the service of doing good; one can simply do the most good one can do within those side constraints.

2. Many EAs are interested in taking into account moral uncertainty, i.e. uncertainty about which moral system is correct. Even if you think the most likely theory is consequentialism, it can be rational to act as if there is a side constraint against killing if you place some amount of credence in a theory (e.g. a deontological theory) on which killing is always quite seriously wrong. The thought is this: if there's some chance that your house will be damaged by a flood, it can be worth it to buy flood insurance, even if that chance is quite small, since the damage if it does happen will be very great. By the same token, even if the theory you think is most probably recommends killing in a particular case, it can still be worth it to refrain, if you also place some small credence in another theory that thinks killing is always seriously wrong. Will MacAskill discusses this in his podcast with Rob Wiblin.

Tl;dr: you might think killing one to save ten is wrong because you're a nonconsequentialist, and this is perfectly compatible with EA. Or, even if you are consequentialist, and even if you think consequentialism sometimes recommends killing one to save ten, it might still be rational not to kill in those cases, if you place even a small credence in some other theory on which this would be seriously wrong.

I'm not sure many EAs will agree with your intuition (If I'm understanding your question correctly) that it's morally wrong to kill one person to save 10. There are certainly some moral philosophers who do, however. This dilemma is often referred to as the "trolley problem", and has had plenty of discussion over the years.

You may find this interesting reading, it turns out people's intuitions about similar problems vary quite a lot based on culture.