There are two types of 401(k) contributions: "elective contributions," which are the part put in by the employee and "nonelective contributions," which are the part put in by the company.
Elective contributions are summed across all the plans she is contributing to. So she can contribute $18,000 minus whatever she put in her 403(b).
Additionally she can contribute 20% of the net profit of the company (before the elective contributions) as nonelective contributions (these contributions must be designated as such). You will notice that the IRS document says 25%, but that's what you can do if her business is incorporated. For a sole proprietorship, nonelective contributions ends up being limited at 20% of profit.
Additionally, the sum of these two and her contribution to her 403(b) cannot exceed $53,000.
Example: line 31 of her schedule C is $30,000 and she has contributed $10,000 to her 403(b).
Maximum contribution to her solo 401(k) is
($18,000 - $10,000) + 0.2 * $30,000 = $14,000
Her total contributions for the year are $10,000 from her 403(b) plus $14,000 in her solo 401(k). This is less than $53,000 so this limit does not bind. If she made a ton of 1099 money, her contribution maximum would follow the above until it hit $53,000 and then it would stop there.
The IRS describes this in detail in Publication 560, which also has a worksheet for figuring out your maximum explicitly. It's unpleasant reading and the worksheets are painful, but if you do it right, it will end up being as I just described it. Using the language of that publication, hers is a "qualified plan" of the "defined contribution" variety.