How should I recover my NTFS partition that I have accidentally deleted on my Mac I have a 2 TB external HDD that was divided in 2 partition:

First partition: 280 GB
Second partition: 1720 GB

I accidentally delete the second partition.

Here are several steps that I already did;

result of diskutil list

~ diskutil list
  /dev/disk0 (internal, physical):
     #:                       TYPE NAME                    SIZE       IDENTIFIER
     0:      GUID_partition_scheme                        *250.1 GB   disk0
     1:                        EFI EFI                     209.7 MB   disk0s1
     2:                 Apple_APFS Container disk1         249.8 GB   disk0s2

  /dev/disk1 (synthesized):
     #:                       TYPE NAME                    SIZE       IDENTIFIER
     0:      APFS Container Scheme -                      +249.8 GB   disk1
                                   Physical Store disk0s2
     1:                APFS Volume Macintosh HD            119.9 GB   disk1s1
     2:                APFS Volume Preboot                 20.5 MB    disk1s2
     3:                APFS Volume Recovery                503.9 MB   disk1s3
     4:                APFS Volume VM                      5.4 GB     disk1s4

  /dev/disk2 (external, physical):
     #:                       TYPE NAME                    SIZE       IDENTIFIER
     0:     FDisk_partition_scheme                        *2.0 TB     disk2
     1:               Windows_NTFS HDD1                    228.4 GB   disk2s1


Here is the result of sudo fdisk /dev/disk2

~ sudo fdisk /dev/disk2
    Disk: /dev/disk2    geometry: 243201/255/63 [3907029167 sectors]
    Signature: 0xAA55
             Starting       Ending
     #: id  cyl  hd sec -  cyl  hd sec [     start -       size]
    ------------------------------------------------------------------------
    *1: 07 1023 254  63 - 1023 254  63 [    206848 -  446126158] HPFS/QNX/AUX
     2: 00    0   0   0 -    0   0   0 [         0 -          0] unused      
     3: 00    0   0   0 -    0   0   0 [         0 -          0] unused      
     4: 00    0   0   0 -    0   0   0 [         0 -          0] unused      


EDIT:

$ sudo dd if=/dev/disk2 bs=512 skip=446333006 count=150000000 | grep -o -a -b "BOOTMGR"

71010552671:BOOTMGR
71010552692:BOOTMGR
150000000+0 records in
150000000+0 records out
76800000000 bytes transferred in 11355.441546 secs (6763277 bytes/sec)
The NTFS volume has been recovered in a TeamViewer session. The method is slightly related to my answer here: Can't see external HDD partition in Disk Utility

Preface:

The NTFS volume was formatted attached to a Mexican-Spanish (or French?) Windows system.

The specific string "BOOTMGR" to find the NTFS Partition Boot Sector with grep wasn't successful because on these systems - as it later transpired - the proper string is "bootmgr" instead.

Assumptions:

The vanished partition and its important blocks weren't overwritten. The partition is situated near the "end" of the disk.



So the following method was used:


Enable and log-in as root and install wxHexEditor
get the device identifier with diskutil list. Below I assume it's disk2.
Open the device disk2 in wxHexEditor, jump to the very end of the disk and backward-search for the string "NTFS" which revealed the (2nd) Partition Boot Sector of the NTFS volume.
With its byte offset the block number of the last NTFS volume block can be determined (byte offset/512 + 1 = block number)
The (2nd) Partition Boot Sector contains the size of the whole NTFS volume in sectors at offset 0x028 and a field length of 8 Bytes and the sector size at offset 0x0B and a field length of 2 Bytes.


Sector size: 00 02 (= 512 Byte)
volume size in sectors was (after a 64bit to decimal conversion) 2047997951+1 blocks (one has to add 1 to the number of blocks because block count starts at 0!)

In Terminal the partition was added with fdisk:

fdisk -e /dev/disk2
edit 2 #add second partition
Partition id ('0' to disable)  [0 - FF]: [0] (? for help) 7 #HPFS/QNX/AUX
Do you wish to edit in CHS mode? [n] n
Partition offset [0 - 3907029167]: [446333006] 1859028992
Partition size [1 - 2048000175]: [2048000175] 2047997952
write
exit

the volume was mounted automatically.
The NTFS volume was checked with Paragon NTFS for Mac with a "no errors" result.




The initial details of at least one of the two deleted partitions posted by the OP were wrong:


First partition: 280 GB
Second partition: 1720 GB


The second partition had and has a size of 1.049 TB only!