Learn German: Schweren Herzens planen wir den Abschied. - With a heavy heart, we are planning the farewell.

This is an "adverbial genitive" of manner. Instead of using a preposition like "with", German sometimes uses the genitive case itself to describe how an action is performed. While the adverbial genitive is often used for time (like eines Tages), it is also used in a few fixed descriptive expressions like this one.

Why does the adjective schweren end in -en rather than -es?

Because there is no article here, you might expect the strong neuter genitive ending -es on the adjective. However, in modern German, when a masculine or neuter noun has its own genitive -s or -es ending (like Herzens), the preceding adjective takes the ending -en instead. You will see this happen frequently in genitive phrases.

Where does the unusual -ens ending on Herzens come from?

Das Herz (the heart) is a unique, irregular noun. It behaves somewhat like an n-declension noun, taking an -en ending in the dative case (dem Herzen). However, in the genitive case, it adds both that -en and the standard neuter -s, resulting in the unique form des Herzens.

Why does the verb planen come before the subject wir?