Apr 19 21:50:04 MacBook-Pro ReportCrash[553]: Process:               macOS Installer [549]
Apr 19 21:50:04 MacBook-Pro ReportCrash[553]: Path:                  /System/Installation/CDIS/macOS Installer.app/Contents/MacOS/macOS Installer
Apr 19 21:50:04 MacBook-Pro ReportCrash[553]: Identifier:            com.apple.macOS-Installer
Apr 19 21:50:04 MacBook-Pro ReportCrash[553]: Version:               1.0 (1004.29)
Apr 19 21:50:04 MacBook-Pro ReportCrash[553]: Build Info:            OSInstaller-1004029000000000~86
Apr 19 21:50:04 MacBook-Pro ReportCrash[553]: Code Type:             X86-64 (Native)
Apr 19 21:50:04 MacBook-Pro ReportCrash[553]: Parent Process:        ??? [527]
Apr 19 21:50:04 MacBook-Pro ReportCrash[553]: Responsible:           macOS Installer [549]
Apr 19 21:50:04 MacBook-Pro ReportCrash[553]: User ID:               0
Apr 19 21:50:04 MacBook-Pro ReportCrash[553]:  
Apr 19 21:50:04 MacBook-Pro ReportCrash[553]: Date/Time:             2018-04-19 14:49:54.196 -0700
Apr 19 21:50:04 MacBook-Pro ReportCrash[553]: OS Version:            Mac OS X 10.13.4 (17E199)
Apr 19 21:50:04 MacBook-Pro ReportCrash[553]: Report Version:        12
Apr 19 21:50:04 MacBook-Pro ReportCrash[553]: Bridge OS Version:     <device not connected>
Apr 19 21:50:04 MacBook-Pro ReportCrash[553]: Anonymous UUID:        FB9E7040-D694-4666-932D-0596AA936FC4
Apr 19 21:50:04 MacBook-Pro ReportCrash[553]:  
Apr 19 21:50:04 MacBook-Pro ReportCrash[553]:  
Apr 19 21:50:04 MacBook-Pro ReportCrash[553]: Time Awake Since Boot: 79 seconds
Apr 19 21:50:04 MacBook-Pro ReportCrash[553]:  
Apr 19 21:50:04 MacBook-Pro ReportCrash[553]: System Integrity Protection: disabled
Apr 19 21:50:04 MacBook-Pro ReportCrash[553]:  
Apr 19 21:50:04 MacBook-Pro ReportCrash[553]: Crashed Thread:        0  Dispatch queue: com.apple.main-thread
Apr 19 21:50:04 MacBook-Pro ReportCrash[553]:  
Apr 19 21:50:04 MacBook-Pro ReportCrash[553]: Exception Type:        EXC_BAD_ACCESS (SIGSEGV)
Apr 19 21:50:04 MacBook-Pro ReportCrash[553]: Exception Codes:       KERN_INVALID_ADDRESS at 0x0000000000000018
Apr 19 21:50:04 MacBook-Pro ReportCrash[553]: Exception Note:        EXC_CORPSE_NOTIFY
Apr 19 21:50:04 MacBook-Pro ReportCrash[553]:  
Apr 19 21:50:04 MacBook-Pro ReportCrash[553]: Termination Signal:    Segmentation fault: 11
Apr 19 21:50:04 MacBook-Pro ReportCrash[553]: Termination Reason:    Namespace SIGNAL, Code 0xb
Apr 19 21:50:04 MacBook-Pro ReportCrash[553]: Terminating Process:   exc handler [0]

Full log on Pastebin: https://pastebin.com/GtkESaWh

Any ideas?

The crash report blames the installer, so the installer ran into a situation it could not cope with.

Can you boot into safe mode (Shift) during startup? If so download the combo update for 10.13.4 and run that.

If not, then the big question is can you boot into recovery mode (⌘r) at startup?

If you can I would first run disk utility and see if it can repair the disk. If it reports errors that can't be fixed, you have a problem as I am not aware of any 3rd-party disk repair utilities that can repair APFS disks (anyone?).

Please tell me you have a current backup that you can restore from?

If not I would be tempted to take it to an Apple Store and see if they can do anything with the drive.

If Disk Utility can fix or finds no issues, I would reinstall MacOS from Recovery Mode. It shoudn't wipe any of your files but depending on what happened I could not guarantee that.

That should get you started.