We know that both of our numbers will need to be negative so that they multiply to get a positive number (the double negatives cancel) but add to get a negative one.
Consider factor pairs of 40.
-40 × -1 = 40 (adds to -41)
-20 × -2 = 40 (adds to -22)
-10 × -4 = 40 (adds to -14)
-5 × 8 = 40 (adds to -13)
Your numbers are -5 and -8.