The answer is that sometimes (often!) you use て-form to describe cause and effect. You can think about it as an extension of connective use to mean 'and (then)', but you do have to be a bit careful about how you use it.
To answer your question directly, in your example, you can essentially translate it as a "so" (or "because" if you reverse the clause order), giving you:
難しすぎてできませんでした.
It was too difficult, so I wasn't able to do it.
I wasn't able to do it because it was too difficult.
The instances where you use the て-form to describe cause and effect are limited to those times when you are not expressing intention or volition. That includes requests, orders, prohibitions etc... The clauses should also come in chronological order.
As such, this most typically is used when you are describing emotions, potential verbs, verbs of state, and things which have already happened (often unfortunate ones...).
For instance, emotion:
ニュースを聞いて、びっくりしました。
I was surprised to hear the news.
(lit. I heard the news, so I was surprised)
potential:
眼鏡{めがね}がなくて、小さい字が読めません。
I don't have my glasses, so I cannot read small characters.
state:
毎日忙しくて、勉強する時間がありません。
I am busy every day, so I do not have time to study.
(unfortunate) past event:
事故があって、電車が遅れてしまいました。
There was an accident, so the train was (regrettably) delayed.
In the following sentences, the starred examples are not grammatical:
① 危ないから、泳がないでください。
*① 危なくて、泳がないでください。
Because it is dangerous, please do not (go) swim(ming).
② 明日、テストがあるから、今日、勉強しなければならない。
*② 明日、テストがあって、今日、勉強しなければならない。
Because I have a test tomorrow, I must study today.
Here, you cannot replace the から with the appropriate て-form, because *① violates the will/intention condition in being a request, and *② violates the chronology condition.
See also: て used as "because"?
Hope that helps!
