If element x bonds covalently with element y, then what must the electronegativity difference between x and y be for this bond to be nonpolar?

The electronegativity difference must be any value from zero to 0.4.

Explanation:

Covalent bond:

It is the bond formed by the sharing of electrons between the atoms.

The covalent bond is polar when the electronegativity difference between the bonded atoms is greater than 0.4.

The polarity is created when one atom is more electronegative and attract the  electron pair to wards itself more than the other bonded atom. Thus it becomes the partial negative while the other less electronegative atom become partial positive.

If the difference is 0-0.4 than the bond is said to be non polar.

Examples:

Electronegativity values of O. F and H are

O = 3.4

H = 2.2

F = 3.98

For O-F

3.98 - 3.4 = 0.58

For H-F

3.98 - 2.2 = 1.78

For H-O

3.4 - 2.2 =  1.2

For H-H

2.2 -2.2 = 0

So H-H is nonpolar.