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Let's assume I've encrypted some text with some 24-byte key using 3DES ECB. Question: is it possible to regain the key if I have both encrypted and decrypted text? Excluding bruteforce.

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That would amount to divination. –  fgrieu Jan 22 at 9:17
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up vote 2 down vote accepted

It is not practically possible. There are several attacks that are slightly faster than bruteforcing $2^{112}$ key candidates, but this is only a small factor. In some sense, they are bruteforce-like, since they require $2^{113}$ smaller steps.

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