Learn Dutch: Wij wilden bij het interessante bedrijf solliciteren. - We wanted to apply at the interesting company.

Wilden is the plural simple past form of the modal verb willen (to want). Since the subject is wij (we), you add an -n to the singular past tense form wilde.

Why does solliciteren go at the very end of the sentence?

This is a strict Dutch word order rule. When you use a conjugated modal verb like wilden in the second position of a sentence, it kicks the main action verb (solliciteren) all the way to the end in its full dictionary form (the infinitive).

Why does interessante have an -e at the end?

Bedrijf is a het-word (het bedrijf). When you use an adjective before a noun, it usually gets an -e ending. The only time you drop the -e is when a het-word is preceded by een (a) or no article at all. Since we are using the specific article het (the) here, interessante keeps the -e.

Why is the preposition bij used here for 'at'?