973+1054+874 add up to 2901, which exceeds 2200 people participating in the survey, implying that 2901-2200=701 people use both Internet Explorer and Firefox; and 2200-874=1326 people use at least one of Internet Explorer or Firefox.
The solution can also be found using a Venn diagram. Draw a circle containing three other circles, two of which interlock. Write 874 in the non-interlocking circle. This is the number of people using neither Firefox nor Internet Explorer, hence 2200-874=1326 people must be using one or the other or both. The interlocking circles produce three zones: zone A is all those exclusively using IE, zone B those exclusively using Firefox, and zone C those using both. Zone C is the overlap between A and B. A+B+C=2200-874=1326. We don't yet know A, B or C, but we know that A+C=973 and B+C=1054. The diagram tells us that, because C is the overlap, the total area containing 1326 people is made up of (A+C)+B or A+(B+C), one complete circle and one "bitten" circle. We know (A+C)+(B+C)=973+1054=2027=A+B+2C. But A+B+C=1326, so C=2027-1326=701. Hence there are 701 people using both browsers.