Don’t Say: This is a problem for Ellen and I to solve.
Say Instead: This is a problem for Ellen and me to solve.

Here’s Why: Let’s apply the rule that pronoun cases are supposed to agree with their roles in the sentence. In this sentence, the subject is the word “this.” “Ellen,” and “I” are subjects too, but they’re subjects of the infinitive “to solve,” so “I,” the subjective case, is incorrect here.
Almost no one would pick the wrong form of the pronoun in this sentence if there weren’t two people involved. You’d say, “this is a problem for me to solve,” using the correct objective case instinctively. But throw another person in there, and everybody squirms, thinking “Ellen and me” sounds funny. We’re often afraid of the word “me,” but “me” is perfectly respectable and hates being shunted aside for no reason.

Tip: Here’s an easy way to figure out whether “I” or “me” is correct when there’s more than one person in your sentence. Ask yourself what form of the pronoun you’d pick if you took
the other person out, just like we did when we dumped poor Ellen. The choice you make between “I” and “me” when there’s no one else involved is the same one you should make when
everyone and your mother are part of the story. Let’s look at a few more examples to cement this down:
Instead of Me and Jerry are leaving, say Jerry and I are leaving.
(Here, the personal pronoun is intended to be the subject of the verb “are,” so you need the subjective case form, “I.” Double-check by using the tip: Would you say, “Me are leaving?” No, you’d say, “I am leaving,” so “I” is correct.)

 Instead of saying It was me, say It was I.

(Remember, you need the subjective case whenever the personal pronoun follows a form of the verb “to be” without the “to” in front, whenever it’s the complement of a linking verb. That’s what we’ve got going on here. The verb “was” in this sentence is of course a form of the verb “to
be.” So we need the subjective pronoun, “I,” instead of the objective form, “me.”)

 Jack and Jill are going with me down the hill.
Jack and I are going down the hill with Jill.
There’s nothing between Laverne and me, I swear!
Will you come to dinner with Sandy and me?
They’ve known Larry and me for years.
Larry and I have known them for years.