According to this IRS publication, you meet the requirements for a partial exclusion if any of the following events occurred during your time of ownership and residence in the home.
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You took or were transferred to a new job in a work location at least 50 miles farther from the home than your old work location. For example, your old work location was 15 miles from the home and your new work location is 65 miles from the home.
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You had no previous work location and you began a new job at least 50 miles from the home.
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Either of the above is true of your spouse, a co-owner of the home, or anyone else for whom the home was his or her residence.
Also the publication mentions, If you didn't sell another home during the 2-year period before the date of sale (or, if you did sell another home during this period, but didn't take an exclusion of the gain earned from it), you meet the look-back requirement. You may take the exclusion only once during a 2-year period. In your case, you sold your second home 4/20 and your previous home 05/18. This is under the two-year period thus does not meet the two-year look-back requirement.
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