Say that one of our odd numbers is #x#. That would mean that the next odd number after #x# would be #x+2# (because odd numbers are separated by an even number).

Since we know that their sum is #-116#, we can set up an equation and solve for #x#:

#x+(x+2)=-116#

#x+x+2=-116#

#2x+2=-116#

#2x+2color(blue)-color(blue)2=-116color(blue)-color(blue)2#

#2xcolor(red)cancel(color(black)+color(black)2color(blue)-color(blue)2)=-116color(blue)-color(blue)2#

#2x=-116color(blue)-color(blue)2#

#2x=-118#

#(2x)/2=(-118)/2#

#(color(red)cancelcolor(black)2x)/color(red)cancelcolor(black)2=(-118)/2#

#x=(-118)/2#

#x=-59#

This is our first odd number. We said that our other odd number would be #x+2#, so, therefore, our numbers are #-59# and #-59+2#, or #-57#. Hope this helped!