In modern English both are used. Technically the most grammatically correct is even to write because it’s based on old Latin grammatical rules so you shouldn’t split an infinitive. That means ‘to’ and the verb should stay together. But, in reality, in modern speech ‘too tired to even write’ sounds completely natural as well.

When used in this sense, "even" is a word Americans are very careless with. You will sometimes see a similar sentence with "even" as the last word. In this example the meaning is not clear to me. Obviously, the implication is that one could write a text in another language but that English would be easier. A clearer meaning might be "I'm too tired even to take off my shoes," a task that is so easy as to clearly indicate how tired one is.

Add this one too, 'I feel too tired to write a text; even in English.' English is so dynamic.