Soft returns/newlines are something of a glitch in reflowable EPUB; there's a checkbox to remove them for a fairly good reason.
The better techniques for controlling line breaks, especially for chapter headings, is to specify left/right margins or use nonbreaking spaces very selectively. In this case, a hard space between the words "MR.[hard space]MCGRATH[hard space]REFUSES[soft space]AN[hard space]INVITATION" would probably work best, but 5-10% side margins might work almost as well. Or in combination.
The attached chapter number is a problem. Only a soft return can create that alignment and create a proper TOC entry. There are other formatting techniques that might work better, such as two styles.
After some tinkering, it looks as if the only way to create the style shown and have a matching TOC is:
Use two styles for the chapter number and chapter title.
Set the chapter title margins to help fold the text, and selective use of hard spaces to hold text together.
In the TOC, ignore the chapter number style and auto-number the chapter entries to match.
— | Word & InDesign to Kindle & EPUB: a Pro Guide (Amazon)