Why is Eric Dale brought back to the firm for just one day?

Summary

1. Eric found out that they have a lot of toxic assets
2. They want to sell them in one day before anyone else finds out
3. Since Eric knows everything, they want him under their control and to keep quiet
4. They use the carrot and stick approach: Either a lot of money or ruin

Why do they need him? What difference does it make that he's back at the company, especially for only one day?

Their plan of selling the assets only works, if the potential buyers don't know that they are toxic. Eric was fired and presents a risk to the firm. He knows their secret and could tell somebody. So they want him back at the company for just one day and a lot of money to specifically do nothing - keep quiet under their control, while they sell the assets.

Explanation

From wikipedia:

Cohen's plan is for the firm to quickly dump all of the toxic assets in a fire sale before the market learns of their worthlessness, thereby limiting the firm's exposure. Tuld favors the plan, comparing the economic situation to one of musical chairs: when the music stops, the last one standing will be left with only toxic, worthless securities.

And snippets from the script:

Scene 60 (71-74), Will and Seth at Eric's "very nice large townhouse":

WILL EMERSON: Jared Cohen called an emergency meeting of the partners tonight. John Tuld has decided to liquidate our entire position.

...

WILL EMERSON: They want me to get you back there, they are worried about you being out here.

("out here" - he was fired, is not under their control and could thwart their plans by telling someone about his discovery.)

ERIC: I signed my papers man, I'm out. They've got nothing on me anymore.

WILL EMERSON: They'll pay...

ERIC looks over at WILL. WILL lets him know with a look that they mean real money.

Their plan mentioned again (I bowdlerized it):

WILL EMERSON: True. Dumping the whole [beep] motherload in one day. [beep] up. Well... alright.

Finally, Will mentions what happens if Eric doesn't come (I had to bowdlerize again):

                     WILL EMERSON
           Tuld doesn't want any loose ends.

                     ERIC
           They fired me Will. [beep] em... [beep] em.

                     WILL EMERSON
           Just come back with them, take the bonus,
           and you're home tonight by five. Either
           that or they are going to fight you on
           everything, the package, the options...

 ERIC drops his head.