Since there will be no capital gain to be reported on the federal tax return your EIC will not be affected by the sale of the home.
Reporting the sale on the federal tax return the gain reported will be 0 on the Form 1040 Line 7. So you will not be affected by the Investment Income limit.
See the Investment Income worksheet in Publication 596 Earned Income Credit (EIC) on page 6 - https://www.irs.gov/pub/irs-pdf/p596.pdf#page=6
